Quadratic Equation Solver
Solve any quadratic equation ax² + bx + c = 0 by factoring, completing the square or the quadratic formula, with the discriminant explained. Try “solve 2x² − 5x + 3 = 0”.
Try an example:
What you can do with the Quadratic Equation Solver
Factoring, completing the square and the quadratic formula.
Enter your values or describe the problem in the calculator above. Review the result and the explanation before using it in homework, study or practical calculations.
Example input
e.g. solve 2x^2 - 5x + 3 = 0
How the Quadratic Equation Solver works
- Write the equation in standard form and identify a, b and c.
- Compute the discriminant b² − 4ac to see whether there are two, one or no real roots.
- Apply x = (−b ± √(b² − 4ac)) ÷ 2a and simplify both roots.
Frequently asked questions
What does the discriminant tell you?
If it is positive there are two real roots, if zero one repeated root, and if negative two complex roots.
Which method should I use?
Factor if the numbers are friendly. The quadratic formula always works, and completing the square is best for vertex form.
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Math Solver can make mistakes. Please double-check important steps and calculations.