Method
Uses the discriminant and quadratic formula to identify and calculate roots.
Numbers / browser tool
Quadratic Equation Solver
Solve ax² + bx + c = 0 and identify its roots.
Use the discriminant and quadratic formula for real or complex roots.
Your inputs stay on your device
Solve a quadratic equation
live resultRoots
Discriminant
x₁ / x₂
Calculations run locally and describe the supplied values only.
Context & Reference
How it works
For solving ax² + bx + c = 0.
calculator guideHow to use it
Use this calculator with your own values, then review the clearly labelled result and copy it when you need it elsewhere.
Understand the result
Results distinguish two real roots, one real root, or a complex pair.
Example
Solve x² − 5x + 6 = 0.
Practical tip
Coefficient a must be non-zero.
Notes
This calculator runs locally in this browser. Coefficient a must be non-zero.
Helpful answers
Frequently Asked Questions
A few useful details beyond the guide above.
It means the equation has no real-number solutions. The solver shows the pair using an imaginary component, so there is no real x-intercept to plot.
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