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 it 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.
Try these 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.
A few good questions
How is the result produced?
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.
Are my inputs sent to a server?
No. Inputs and results are processed locally and are not uploaded or included in telemetry. Copying or downloading is your choice.
What are the limits of this tool?
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.
Updated September 19, 2026