Quadratic Equation Calculator
Enter the coefficients a, b and c to solve any quadratic equation — including ones with complex roots.
Updated
Formula
x = (−b ± √(b² − 4ac)) ÷ 2a
Discriminant D = b² − 4ac
D > 0: two real roots. D = 0: one repeated root. D < 0: two complex roots.
Examples
x² − 3x − 10 = 0
1x² − 3x − 10 = 0: x = 5 or x = -2
x² + 2x + 5 = 0 (complex)
1x² + 2x + 5 = 0: x = -1 + 2i or x = -1 − 2i (complex roots)
2x² − 8x + 8 = 0
2x² − 8x + 8 = 0: x = 2 (one repeated root)
Important information
- The vertex is the turning point of the parabola y = ax² + bx + c; it's a minimum if a > 0 and a maximum if a < 0.
Frequently asked questions
What is the quadratic formula?
x = (−b ± √(b² − 4ac)) / 2a. It solves every equation of the form ax² + bx + c = 0.
What does a negative discriminant mean?
The parabola doesn't cross the x-axis, so there are no real solutions — the roots are complex numbers.
Why can't a be zero?
Then there's no x² term and the equation is linear (bx + c = 0), not quadratic.
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