Faith vs. works.  Christians have debated this topic for two thousand years and still do.  At the heart of the debate you have two (seemingly) opposing sides:

Team Faith says works are not required for salvation.  Salvation is received by grace through faith alone (John 6:28-29, Ephesians 2:8-9, Romans 4:5, Romans 11:6, Galatians 2:21).  They believe that making works a requirement for salvation ignores the very message of the Gospel that Jesus died for our sins and rose again (1 Corinthians 15:1-4), which the Apostle Paul calls "of first importance."  This is Christianity 101.  If Jesus died for your sins as a substitutionary sacrifice how can sin or lack of works now separate the Believer from God since our sins were the very reason He died?  Isn't the point of the Cross that under the law works were a requirement for salvation and because we couldn't keep the law perfectly (James 2:10) Jesus did it for us?

Team Works doesn't deny that faith is necessary for salvation, but adds performing good works and/or avoiding sin enough as necessary components of salvation.  The works-righteousness side relies heavily on James 2:14-24 and Philippians 2:12, which both prima facie seem to indicate the opposite of such often referenced sola fide verses as Ephesians 2:8-9 and Romans 4:5.  This is the position taken by Roman Catholic and Eastern Orthodox theologians, as well as some Protestants such as N.T. Wright.

While there are essentially two sides to the debate, there are actually three ways to explain the relationship between faith and works, because Team Faith can be further split into two categories: first, those who think that faith and salvation have no relationship to works and thus grace is a license to sin (these are called antinomians: anti = against and nomian = law, so "against law").  Second, those who believe we are saved by faith alone, but the type of faith that saves is a faith that consequentially results in obedience to God and thus good works.  The second view differentiates between a professed faith and a penitent faith.  To summarize the three views:

1. Faith + works = salvation.  This is Team Works and is the official doctrine of the Roman Catholic Church per the sixth session of the Council of Trent (1547).  Eastern Orthodox and some Protestant churches also subscribe to this view.  It uses James 2:14-24 as the chief proof text.

2. Faith = salvation - works.  This is one of the two camps in Team Faith.  Unfortunately for this team, it is condemned at least twice in the Bible (Romans 6:1-2, Jude 1:4), and universally by the early Church.  The Bible repeatedly describes the Believer's life as characterized by love and good deeds - avoidance of sin and works stemming from faith.  For this reason antinomianism is not compatible with God's Word.  There are virtually no denominations or churches that officially subscribe to this view, although there are a large and growing number of churches and professing Christians who in practice are antinomians because they justify things that the Bible clearly defines as sin (e.g. homosexuality, adultery, abortion, obscenity, etc).

3. Faith = salvation + works.  This is the position held by a large majority of Protestant groups including Evangelicals, Anglicans, Pentecostals, and Lutherans.  It is also the official position of most Protestant denominations even if many Protestants themselves may reject the view in favor of either view #1 or view #2.  In my understanding this is also the view espoused in the Bible and in the early Church, which over centuries was diluted until Luther and Melanchthon attempted to restore the doctrine to the Church.  Galatians 2:11-3:26, Romans 3:21-5:2, and Ephesians 2:8-9 are proof texts.

For argument's sake let's all agree that view #2 is not biblical and is in fact heresy (as evidenced by many of the same scriptures that view #1 emphasizes).  We are left with #1 and #3.  Here are the reasons why I believe #3 is the biblical view:

1. It is the only view that can reconcile all scriptures.  View #1 can only sustain itself by ignoring and de-emphasizing literally dozens and dozens of scriptures that indicate salvation is wrought by faith in or belief in Jesus.  Some of the passages ignored include long discourses on faith apart from works such as the aforementioned Galatians 2:11-3:26 and Romans 3:21-5:2.  View #3 can actually reconcile James 2:14-24 prima facie, whereas view #1 cannot reconcile the Galatians, Romans, and Ephesians passages prima facie.  View #3 can also reconcile Philippians 2:12, because the Greek κατεργάζεσθε means "work out" (your salvation), not "work for" (your salvation).

2. It is the only view that preserves the simple Gospel message.  In 1 Corinthians 15:3-4 the Gospel is defined simply as Jesus dying for our sins, being buried, and rising again.  Arguing that not sinning or avoiding sin enough is how one obtains eternal life makes the Gospel pointless since that is the very reason Christ died (Galatians 2:21).  View #1 proponents attempt in a variety of ways to explain how we are saved by God's grace yet works are also necessary, but as the Apostle Paul explains, any mixture of grace and works defeats the very meaning of grace in the first place (Romans 11:6).  Paul appears to demonstrate the absurd dichotomy between faith and works in Galatians 3:1-6.  You can't have it both ways.  There is no compromise.  You can't simultaneously maintain that Jesus paid the price for your sins and yet you still have to pay.

3. It is the only view that correctly understands and defines grace.  The Bible is crystal clear that we are saved by God's grace which came through Christ's atoning sacrifice and resurrection.  Even the Catechism of the Catholic Church teaches this.  Yet, because of the absurdity of saying we are saved by grace and works, some theologians have changed the basic, general understanding of what the word grace means.  In a dictionary or in common conversation grace simply means "unmerited favor" or "undeserved kindness."  Yet to the works-righteousness theologian they tag "sanctifying" onto "grace" to define it as something else entirely: fuel in your spiritual tank to keep you going.

4. Sola fide has more supporting scriptures.  I don't offer this as proof because every verse must be accounted for, but for argument's sake, even if every verse that indicated works were necessary and every verse that indicated faith was necessary could not be reconciled, sola fide would still have more supporting verses.

There are 24 verses that seem to indicate the necessity of works:

James 2:14
James 2:20
James 2:24
James 2:26
Revelation 2:23
Revelation 3:2
Matthew 3:10 (good fruit necessary)
Matthew 6:15
Matthew 13:41 (all who do evil)
Luke 3:9 (good fruit necessary)
Philippians 2:12
Hebrews 10:26 (any sin after conversion; see Hebrews 10:39)
Revelation 20:12 (judged according to deeds)
Revelation 20:13 (judged according to deeds)
1 John 2:4
1 John 2:5
1 John 3:6 (no one who continues to sin)
1 John 3:7
1 John 3:8
1 John 3:9 (no one who continues to sin)
1 John 3:15
1 John 4:20
1 John 5:18 (no one who continues to sin)
3 John 1:11

Yet there are 88 verses that indicate the exclusive necessity of grace, faith, or belief (x represents where condemnation is actually tied to unbelief rather than bad deeds):

John 6:29
Romans 3:20
Romans 3:28
Romans 4:2
Romans 4:6
Romans 9:32 X
Romans 11:6
Galatians 2:16 X
Galatians 3:2
Galatians 3:5
Galatians 3:10 X
Ephesians 2:9
Matthew 9:2
Mark 2:5
Luke 5:20
Luke 7:50
Acts 15:9
Acts 20:21
Acts 26:18
Romans 1:17
Romans 3:22
Romans 3:25
Romans 3:26
Romans 3:27
Romans 3:30
Romans 4:5
Romans 4:9
Romans 4:11
Romans 4:13
Romans 4:14
Romans 4:16
Romans 5:1
Romans 5:2
Romans 9:30
Romans 10:10
Romans 11:20
Galatians 3:8
Galatians 2:21
Galatians 3:11 X
Galatians 3:14
Galatians 3:22
Galatians 3:24
Galatians 3:26
Galatians 5:6
Ephesians 2:8
Ephesians 3:12
Ephesians 3:17
Philippians 3:9
2 Timothy 3:15
Hebrews 10:39 X
1 Peter 1:9
Luke 8:12 X
John 1:12
John 3:15
John 3:16
John 3:18 X
John 3:36 X
John 5:24
John 6:29
John 6:40
John 6:47
John 8:24 X
John 11:25
John 11:26
John 20:31
Acts 10:43
Acts 11:17
Acts 13:39 X
Acts 15:11
Acts 16:31
Romans 1:16
Romans 4:3
Romans 4:24
Romans 9:33
Romans 10:4
Romans 10:9
Romans 10:11
1 Corinthians 1:21
1 Corinthians 15:2 X
Ephesians 1:13
2 Thessalonians 2:12 X
2 Thessalonians 2:13
1 Timothy 1:16
Hebrews 4:3 X
James 2:23
1 John 5:1
1 John 5:5
1 John 5:13
Hebrews 3:19 X

And since there are 88 verses that indicate grace, faith, or belief are exclusively necessary for salvation, and 0 verses indicating the necessity of works apart from faith, that tells me the biblical equation cannot be faith + works = salvation.