About this quadratic equation solver
Solve a quadratic equation in the form ax² + bx + c = 0 for its roots, whether they're two real numbers, one repeated real root, or a complex conjugate pair. Enter the three coefficients a, b, and c, and this tool computes the discriminant b² − 4ac and applies the quadratic formula, showing complex roots in a + bi form when the discriminant is negative. Use this workspace to prepare a result you can review before putting it to use. All processing takes place on your device, without an account or an upload of your inputs. Check the examples to understand the expected output, read the limitations for the supported scope, and reset the form when you want to start a separate task.
How the quadratic equation solver works
Computes the discriminant b² − 4ac, then applies the quadratic formula x = (−b ± √discriminant) / (2a); a negative discriminant gives a complex conjugate pair instead of real roots.
Quadratic Equation Solver examples
a=1, b=-3, c=2
Roots 2 and 1
a=1, b=2, c=5
Roots −1 + 2i and −1 − 2i
Limitations & privacy
Coefficient a must not be zero — an equation with a=0 is linear, not quadratic. Coefficients are limited to ±1,000,000,000, and complex-root values are rounded to 4 decimal places.
Inputs and results stay in this browser. Only tool identifiers are stored for your recently used tools. You can clear that history from the directory.
Quadratic Equation Solver: frequently asked questions
How does the quadratic equation solver work?
Computes the discriminant b² − 4ac, then applies the quadratic formula x = (−b ± √discriminant) / (2a); a negative discriminant gives a complex conjugate pair instead of real roots.
What can I inspect in the quadratic equation solver result?
The quadratic solution steps helps you check the result before using it. Coefficient a must not be zero — an equation with a=0 is linear, not quadratic. Coefficients are limited to ±1,000,000,000, and complex-root values are rounded to 4 decimal places.
Does the quadratic equation solver upload my input?
Processing happens in your browser. No tool input or output is uploaded to a server. Use Reset to clear the current workspace before starting a separate task.
Updated September 20, 2026