Quadratic Equation Solver
Enter the coefficients a, b and c for an equation in the form ax² + bx + c = 0 to get the roots — real or complex — with full step-by-step working shown.
How to Use the Quadratic Equation Solver
- Write your equation in the standard form ax² + bx + c = 0.
- Enter the values of a, b and c into the three boxes (a cannot be 0).
- Click "Solve Equation".
- Read the roots and the full step-by-step working, including the discriminant and square root calculation.
Why Use This Tool?
What is the discriminant and why does it matter?
The discriminant is the value b² − 4ac. It tells you what kind of roots the equation has before you even finish solving: a positive discriminant means two distinct real roots, zero means exactly one repeated real root, and a negative discriminant means two complex (imaginary) roots. This tool always shows the discriminant first so you can see exactly why the final answer takes the form it does.
Does it handle complex roots?
Yes. When the discriminant is negative, the square root of a negative number isn't a real number, so the roots are expressed in the form a ± bi, where i is the imaginary unit. The tool calculates both the real part and the imaginary part for you and shows the working clearly.
What if I enter 0 for "a"?
If a = 0, the equation is no longer quadratic — it becomes linear (bx + c = 0). The tool will let you know so you can adjust your input, since the quadratic formula requires a non-zero leading coefficient.
Is this solver free for students and teachers?
Absolutely. It's 100% free, runs entirely in your browser with no signup, and is designed to help students check homework answers and teachers quickly generate worked examples for class.