About this Quadratic Equation Solver
Quadratic Equation Solver calculates the discriminant and returns two real roots, one repeated root, or a complex-conjugate pair.
Formula or method
x = (−b ± √(b²−4ac)) ÷ (2a).
Example
x² − 5x + 6 = 0 has roots 2 and 3.
Common uses
- Check algebra exercises.
- Identify whether roots are real or complex.
- Verify the quadratic formula.
How to use this tool
- Enter the values or text requested by the calculator.
- Choose units or options when the tool provides them.
- Select the calculation button and review the result.
- Use the formula, example and notes on this page to check whether the result fits your situation.
Important note
Coefficient a must not be zero; if it is zero, the equation is not quadratic.
Frequently asked questions
What does a negative discriminant mean?
It means the quadratic has two complex-conjugate roots rather than real roots.
Can coefficient a be zero?
No. With a = 0 the equation becomes linear and should be solved as a different problem.