How to Solve Quadratic Equations

A quadratic equation has the form ax² + bx + c = 0, where a is not zero. Its roots can be found using the quadratic formula.

The quadratic formula

The roots are x = (−b ± √(b² − 4ac)) / (2a). The expression inside the square root is called the discriminant.

What the discriminant tells you

• Positive: two distinct real roots.
• Zero: one repeated real root.
• Negative: two complex conjugate roots.

Example

For x² − 5x + 6 = 0, a=1, b=−5 and c=6. The discriminant is 25 − 24 = 1, so the roots are (5 ± 1)/2: x=3 and x=2.