# Quadratic equation solver

> Display roots, discriminant and substitution checks.

[Open tool](https://www.toolcabana.com/mt/quadratic-equation-solver) · [Mathematics](https://www.toolcabana.com/mt/category/mathematics)

Tool ID: quadratic-equation-solver. Requested language: mt. Description language: en. Complete guide translation: no; untranslated sections use English.

## Overview (en)

The Quadratic equation solver takes the coefficients a, b and c of ax² + bx + c = 0 and returns the discriminant and the roots. Real roots come with residuals that substitute each root back into the equation as a check. When the discriminant is negative, it shows the complex pair as real part plus or minus imaginary part times i.

## Supported tasks (en)

Display roots, discriminant and substitution checks.

## Steps (en)

1. Enter the requested values in the settings panel.
2. Set a, b, c.
3. Run quadratic equation solver, review the output, then use the available copy or download controls.

## Settings

- a (en; key: a; type: number); minimum: -1000000000000; maximum: 1000000000000
- b (en; key: b; type: number); minimum: -1000000000000; maximum: 1000000000000
- c (en; key: c; type: number); minimum: -1000000000000; maximum: 1000000000000

## Limitations (en)

Local bounded calculations. Numeric inputs must be finite and within the visible ranges. Lists and tables have operation-specific limits. Models, estimates and supplied rates must be checked against your intended use.

## Privacy and connections (en)

This operation processes its source in your browser. Copy and download are explicit actions; source input is not saved in an account or history.

## Questions (en)

### How do I solve a quadratic equation with this calculator?

Enter a, b and c from ax² + bx + c = 0. With the defaults a = 1, b = -3 and c = 2, the solver returns a discriminant of 1 and roots 2 and 1, with residuals of 0 confirming both.

### What does a negative discriminant mean?

The equation has no real roots. The solver then shows two complex roots in the form -b/(2a) plus or minus a value times i, where that value is the square root of the negative discriminant divided by the absolute value of 2a.

### Why does the solver show residuals?

A residual is the value of ax² + bx + c after plugging in a computed root. It should be 0 or very close to it. The solver uses a numerically stable form of the quadratic formula to keep residuals small.

### Where is my input processed?

This operation processes its source in your browser. Copy and download are explicit actions; source input is not saved in an account or history.

### What are the input limits?

Local bounded calculations. Numeric inputs must be finite and within the visible ranges. Lists and tables have operation-specific limits. Models, estimates and supplied rates must be checked against your intended use.

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