Solve ax2 + bx + c = 0 over the reals

Students, teachers and engineers use it to verify the real solutions of ax2 + bx + c = 0 during an exercise or technical calculation.

Solve ax2 + bx + c = 0 over the reals. Everything runs in your browser, so the values you enter are never uploaded, shared, or stored.

How to use

Enter coefficients a, b and c for the equation ax2 + bx + c = 0, one value per line in the input area.
Check that coefficient a is not zero, because otherwise the equation is no longer quadratic and the calculation changes.
Run the calculation and read the result shown beside the input, including the discriminant and the real roots.
Clear the fields to test another equation, or import a small text file containing the values.

Example

With the sample values, the equation has two real roots, and the output should show the discriminant and the solutions. Look at how a negative discriminant is handled, then change the coefficients to explore a case with no real solution or a repeated root. Test a few values to see how the display changes.

Input

1
-3
2

Output

Discriminant: 1
x1: 1
x2: 2

Limits and formats

The tool solves over the real numbers, so it does not provide complex roots.
Coefficients must be entered as numbers; a misplaced decimal separator can change the result.
When the equation comes from a real-world measurement, check whether rounding affects the answer.
File import accepts text, CSV, JSON, Markdown, XML, YAML or YML, but the data must remain simple.

Where processing happens

The quadratic solver runs entirely in your browser. The coefficients you type or import are not sent to an external service or stored after the page is closed. You can close the tab without leaving the coefficients behind.

Frequently asked questions

What does the discriminant tell me?

It indicates how many real solutions the equation has. A positive value means two real roots, zero means one repeated root, and a negative value means no real solution.

Can I use the tool for homework?

It is useful for checking your solutions, but you should still write the method yourself. Teachers usually expect the reasoning, not only the final numbers, and the tool does not show every intermediate step.

Why does the result look rounded?

Some roots are irrational and cannot be written exactly as short decimals. The displayed value is likely an approximation, so use more precision or keep the exact form when accuracy matters.