# How to Solve a Quadratic Equation Using the Quadratic Formula

## Solving a Quadratic Equation Using the Quadratic Formula

The quadratic formula is a way of solving a quadratic equation.

Consider a quadratic equation in standard form:

Solving the quadratic equation means finding the values of **x**, called *roots*, that make this equation true (i.e. makes the left hand side equal to 0.)

The formula below will find the two roots of the equation:

There are two roots because the **±** symbol means consider it as a **+** one time and as a **−** another time.

## How to Solve Quadratic Equations Using the Quadratic Formula

Solving a quadratic equation using the quadratic formula is easy.

### Question

Solve the quadratic equation shown below using the quadratic formula.

### Step-by-Step:

# 1

Compare the quadratic equation in the question with the standard form.

2x^{2} −5x + 2 = 0 ⇔ ax^{2} + bx + c = 0

Find the values of **a**, **b** and **c**.

**a** = 2, **b** = −5, **c** = 2

# 2

Use the formula.

# 3

Substitute a, b and c into the formula. In our example, a = 2, b = −5 and c = 2.

# 4

Find the root that comes from turning the ± into a +.

**x = 2** is a root of the quadratic equation.

# 5

Find the root that comes from turning the ± into a −.

**x = ^{1}⁄_{2}** is a root of the quadratic equation.

### Answer:

We have solved the quadratic equation:

**x = ^{1}⁄_{2}**,

**x = 2**.