Quadratic Equation Solver
Roots, discriminant and vertex for any ax² + bx + c = 0.
Two real roots
x = 4, -1
Discriminant
25
Vertex
(1.5, -6.25)
Sum of roots
3
Product of roots
-4
ShowHide the working
- 1Discriminant = b² − 4ac = 25 (> 0, two real roots)
- 2x = (−-3 ± √25) ÷ 2
Formula
x = (−b ± √(b² − 4ac)) ÷ 2aHow it works
Solves any quadratic ax² + bx + c = 0, reporting real or complex roots plus the vertex and discriminant.
Example
x² − 3x − 4 = 0 has roots x = 4 and x = −1.
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About the Quadratic Equation Solver
Roots, discriminant and vertex for any ax² + bx + c = 0. It sits in the Math & Algebra section of NWS Calc, a free collection of calculators that run entirely in your browser. There is no signup, no paywall and no tracking — open the page, enter your numbers, get an answer.
Frequently asked questions
- Is the Quadratic Equation Solver free to use?
- Yes. Every calculator on NWS Calc is completely free, with no signup, no usage limits and no ads.
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- No. The Quadratic Equation Solver runs entirely in your browser using JavaScript. Nothing you type is uploaded, logged or stored on a server.
- Can I use the Quadratic Equation Solver on my phone?
- Yes. The page is fully responsive and works in any modern mobile or desktop browser — there is nothing to install.
- What else is in Math & Algebra?
- Equations, fractions, primes, roots, sequences and number theory. You can browse the full Math & Algebra category for related calculators.