Step-by-Step: The Quadratic Formula
- Identify a, b, and c from the standard form ax² + bx + c = 0.
- Calculate the discriminant, b² − 4ac.
- Plug into the quadratic formula and simplify.
Worked Example
Solve 2x² − 4x − 6 = 0.
a=2, b=−4, c=−6. Discriminant = (−4)² − 4(2)(−6) = 16 + 48 = 64.
x = (4 ± √64) / 4 = (4 ± 8) / 4
x = 3 or x = −1
Frequently Asked Questions
Should I always use the quadratic formula?
Try factoring first if the numbers look clean — it's faster. Fall back on the formula whenever factoring isn't obvious within a few seconds.
What if the equation isn't already set to zero?
Move all terms to one side first so the equation reads "= 0" before identifying a, b, and c — this is a required first step before applying the quadratic formula.
