The quadratic formula solves any quadratic equation of the form ax² + bx + c = 0, where a ≠ 0. The discriminant (b² − 4ac) determines whether the equation has two real roots, one real root, or two complex roots.
Solve x² + 5x + 6 = 0
a=1, b=5, c=6. x = (−5 ± √(25−24)) / 2 = (−5 ± 1) / 2. x = −2 or x = −3
Solve 2x² − 4x − 6 = 0
a=2, b=−4, c=−6. x = (4 ± √(16+48)) / 4 = (4 ± 8) / 4. x = 3 or x = −1
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