Everyday Tools

Quadratic Formula Calculator

Solve a quadratic equation from coefficients a, b, and c using the quadratic formula.

Updated April 13, 2026
Free online tool
Planning and research use

Why this page exists

Quadratic equations are easier to solve when the discriminant and roots are calculated directly instead of worked out line by line every time. This calculator helps visitors solve a quadratic equation from coefficients a, b, and c and clearly shows whether the roots are real or complex.

Interactive tool

Run the estimate

Enter your numbers and read the result first, then use the sections below to understand what affects the outcome.

Calculator

Quadratic formula calculator

Solve a quadratic equation from coefficients a, b, and c using the standard quadratic formula.

Result

Two distinct real roots

Estimated roots based on the quadratic formula applied to the coefficients entered.

Discriminant1.0000

Root 13.0000

Root 22.0000

Solution formatTwo distinct real roots

For 1.00x^2 + -5.00x + 6.00 = 0, the discriminant comes to 1.0000.
A positive discriminant means the equation has two distinct real roots.
Use the result to check algebra work quickly, including whether the equation has two real roots, one repeated root, or a complex pair.

This is a standard algebra tool. The result depends on the coefficients entered, and the equation is only quadratic when a is not zero.

Planning note

Last updated April 13, 2026. Use this tool to compare scenarios and plan ahead, then confirm important details with the lender, employer, insurer, contractor, or other qualified provider involved in the final decision.

How it works

What the calculator is doing

Enter coefficients a, b, and c from a quadratic equation in standard form.

The calculator finds the discriminant.

It then applies the quadratic formula and shows the resulting real or complex roots in a readable format.

Understanding your result

This is standard algebra. The equation is only quadratic when coefficient a is not zero, and the discriminant determines whether the roots are real or complex.

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Examples

Ways people use this tool

Example scenarios help turn a quick estimate into a more useful comparison or planning step.

Check homework or worksheet roots quickly

A direct quadratic-formula result can save time when verifying algebra work.

See how the discriminant changes the answer

The calculator makes it easier to see whether the equation has two real roots, one repeated root, or a complex pair.

Use it with other coordinate or algebra tools

Quadratic work often connects with graphing, slope, midpoint, or distance questions later on.

FAQ

Common questions

What does the discriminant tell me?

It tells you whether the quadratic has two real roots, one repeated real root, or two complex roots.

Why does coefficient a matter so much?

The equation is only quadratic if a is not zero. If a is zero, the quadratic formula no longer applies.

Can this calculator show complex roots?

Yes. If the discriminant is negative, the calculator shows the roots in complex-number form.

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Keep comparing

Use these related tools to compare nearby scenarios, check a second estimate, or keep narrowing down the right decision.

Everyday ToolsUpdated April 12, 2026