Quadratic Equation Solver
Solve ax² + bx + c = 0, with the discriminant and steps.
What is a quadratic equation solver?
A quadratic equation solver finds the values of x that satisfy ax² + bx + c = 0. It shows the roots, the discriminant and the steps of the quadratic formula.
How to use the quadratic equation solver
Enter the values of a, b and c, then click Solve. The solver shows the roots and the working, step by step.
Quadratic formula
x = (−b ± √(b² − 4ac)) ÷ 2a. The discriminant, b² − 4ac, tells you how many real roots there are: positive means two real roots, zero means one repeated root, and negative means no real roots.
Example
x² − 5x + 6 = 0 has a = 1, b = −5 and c = 6. The discriminant is 25 − 24 = 1, so the roots are x = 3 and x = 2. It factors as (x − 2)(x − 3) = 0.
Frequently Asked Questions
What are the roots of x²−5x+6?
The roots of x² − 5x + 6 = 0 are 2 and 3. Try it on the solver above.
What is the discriminant?
The discriminant is b² − 4ac. It tells you how many real roots a quadratic has: two if it is positive, one if it is zero, and none if it is negative.
What if the discriminant is negative?
If the discriminant is negative, the equation has no real roots. The solver tells you this and shows the discriminant.
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