Quadratic Equation Solver
The Quadratic Equation Solver finds the roots of any equation in the form ax² + bx + c = 0 using the quadratic formula, and shows real or complex solutions with the working.
The quadratic formula
Enter the coefficients a, b, and c and the solver applies x = (−b ± √(b² − 4ac)) / 2a. The expression under the root, b² − 4ac, is the discriminant, and it tells you what kind of answers to expect before you even finish.
Reading the discriminant
- Positive - two distinct real roots (the parabola crosses the x-axis twice).
- Zero - one repeated real root (it touches the axis once).
- Negative - two complex conjugate roots (it never crosses the axis).
The solver reports the discriminant, the roots, and the vertex, so it doubles as a study aid rather than just an answer box.
Frequently Asked Questions
What is the discriminant and why does it matter?
The discriminant is b²−4ac. Its sign tells you whether the equation has two real roots, one repeated root, or two complex roots.
Can it solve equations with complex roots?
Yes. When the discriminant is negative, it returns the two complex conjugate solutions rather than saying there is no answer.
What if a is zero?
If a is 0 the equation is linear, not quadratic. The solver handles that case as bx + c = 0 with a single root.
Does it show the steps?
It shows the discriminant, both roots, and the vertex of the parabola, so you can follow how the answer was reached.
Related Calculators Tools
Browse all Calculators tools →
Privacy-first: client-side tools process your input in your browser. Free to use, no sign-up. See our Privacy Policy and Disclaimer.