Quadratic Equation Calculator

Solve ax² + bx + c = 0.

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Formula • Worked example • Interpretation

Solve a quadratic equation

A quadratic equation has the form ax² + bx + c = 0 where a is nonzero.

Discriminant D = b² − 4ac. Roots = (−b ± √D) / (2a). If D < 0, the roots are complex.

For x² − 5x + 6 = 0, a=1, b=−5, c=6, so D=1 and the real roots are x=2 and x=3.

D > 0 means two distinct real roots; D = 0 means one repeated real root; D < 0 means no real roots.

Include the sign on b and c; for example, enter −5 rather than 5 for the middle coefficient in the worked example.

If a = 0, the equation is linear and the quadratic formula does not apply. Very large or nearly equal values can cause numerical precision issues.

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