Quadratic Equation Solver (with Steps)
Enter the coefficients of ax² + bx + c = 0 and get the discriminant, both roots and the full working using the quadratic formula.
The quadratic formula
For any equation ax² + bx + c = 0 with a ≠ 0, the solutions are x = (−b ± √(b² − 4ac)) ÷ 2a.
What the discriminant tells you
- D = b² − 4ac > 0: two different real roots.
- D = 0: one repeated real root.
- D < 0: no real roots; two complex conjugate roots.
Worked example
Solve x² − 5x + 6 = 0. Here a = 1, b = −5, c = 6. D = 25 − 24 = 1. So x = (5 ± 1) ÷ 2, giving x = 3 and x = 2. Check: 3² − 15 + 6 = 0.
More practice: Solved quadratic equation examples. For cubic, quartic and other equation types, use the Equations tool in the full Calvo calculator.
FAQ
How do I solve a quadratic equation?
Write it as ax² + bx + c = 0, compute the discriminant b² − 4ac, then apply x = (−b ± √D) / 2a.
What if the discriminant is negative?
Then the equation has no real solutions. It has two complex roots of the form p ± qi.
What if a = 0?
Then it is not quadratic. It becomes the linear equation bx + c = 0 with solution x = −c/b.
Can I use decimals or fractions?
Yes, decimals and negative numbers work. Convert fractions to decimals first.