What is a quadratic equation?

A quadratic equation is a second-degree equation of the form ax² + bx + c = 0, where a ≠ 0.

How are the roots found?

Using the quadratic formula: x = (-b ± √(b² − 4ac)) / (2a).

What does the discriminant mean?

The discriminant is b² − 4ac. It determines whether the equation has two real roots, one repeated real root, or two complex roots.

Can this calculator show complex roots?

Yes. If the discriminant is negative, the calculator shows complex roots in a + bi form.

Are my coefficients stored?

No. Calculations run locally in your browser and are not stored or transmitted.

Quadratic Equation Calculator

Enter coefficients a, b, and c to solve a quadratic equation of the form ax² + bx + c = 0.

Rounding

Result will appear here.

Metric	Value

Uses the quadratic formula: x = (-b ± √(b² − 4ac)) / (2a)

Privacy: calculations run locally in your browser. No coefficients are stored or transmitted.

How it works

First compute the discriminant:
D = b² − 4ac
Then apply:
x = (-b ± √D) / (2a)

Examples

x² − 3x + 2 = 0 → roots: 1 and 2
x² + 2x + 1 = 0 → repeated root: -1
x² + x + 1 = 0 → complex roots

When to use this tool

This tool is designed for quick, practical tasks such as everyday calculations, data formatting, or simple conversions. It is best used when you need fast results without installing software or using complex tools.

When to use

Quick checks or one-time calculations
Validating or converting data before using it elsewhere
Simple tasks that do not require advanced software

When not to use

Critical financial, legal, or medical decisions
Large-scale or automated processing
Situations requiring guaranteed precision beyond basic validation

Always review results before using them in important contexts.

About this tool

This tool helps you perform quick utility operations directly in your browser. It runs entirely in your browser without sending data to a server.

You can use this tool when handling simple tasks without installing additional software. The results should be interpreted as a processed output based on your input data.

FAQ

What is a quadratic equation?
A quadratic equation is a second-degree equation of the form ax² + bx + c = 0, where a ≠ 0.
How are the roots found?
Using the quadratic formula: x = (-b ± √(b² − 4ac)) / (2a).
What does the discriminant mean?
The discriminant is b² − 4ac. It determines whether the equation has two real roots, one repeated real root, or two complex roots.
Can this calculator show complex roots?
Yes. If the discriminant is negative, the calculator shows complex roots in a + bi form.
Are my coefficients stored?
No. Calculations run locally in your browser and are not stored or transmitted.