Use the Quadratic Equation Solver
Solve any quadratic equation ax²+bx+c=0. Get real or complex roots, the discriminant, vertex, axis of symmetry and factored form with step-by-step working.
- Free to use
- No signup
- Nothing to install
- Runs in your browser
Illustration. Open the tool for the real thing.
What is the Quadratic Equation Solver?
A quadratic equation has the form ax² + bx + c = 0, where a is not zero. Its solutions (roots) are given by the quadratic formula x = (−b ± √(b² − 4ac)) / 2a. The part under the root, b² − 4ac, is the discriminant, and it tells you whether the roots are two real numbers, one repeated real number or a complex pair.
Enter the coefficients a, b and c and this solver shows the discriminant, both roots (including complex roots written with i), the vertex and axis of symmetry of the parabola, the y-intercept and the factored form where it exists — with the working written out.
3 steps to your result
Open the tool and follow along. Nothing to install.
What you get
Handles every case, including negative discriminants.
Vertex, axis of symmetry and y-intercept.
Shown whenever the roots are real.
The quadratic formula filled in with your numbers.
AZRS tools are free to open and use.
It opens in your browser, so there is nothing to download.
Used for
Pick one to see how it fits.
How it compares
A plain look at this tool next to the usual alternative.
| This calculator | Desktop software | |
|---|---|---|
| Install | Nothing to install | Usually an app or program to install |
| Account | No signup | Depends on the product |
| Cost | Free to use | Free or paid, depends on the product |
| Where it runs | In your browser tab | On your computer |
Questions people ask
What is the discriminant?
b² − 4ac. Positive means two real roots, zero means one repeated root, negative means complex roots.
What if a = 0?
The equation is linear, not quadratic; the tool will tell you and solve it as linear.
What are complex roots?
Roots involving i, the square root of −1, which occur when the parabola does not cross the x-axis.
How do I find the vertex?
The x-coordinate is −b / 2a; substitute it to find y.
Can I use decimals and fractions?
Yes, enter them as decimals.
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