# Solve Quadratic Equations By Formula

Before viewing this page, it would be helpful to learn how to Solve Quadratic Expressions By Factorizing.

**Quadratic equations** have a **variable with a power of 2** and are in the form:

**ax ^{2} + bx + c = 0**

In the quadratic equation x^{2} + 9x + 20 = 0,

a = 1

b = 9

c = 20.

The **formula** to solve a quadratic equation is:

x = | –b ± √ | b^{2} – 4ac |

2a |

## Example One - Solve by Factorization

Factorize and solve x^{2} + 9x + 20 = 0

**Answer:**

x^{2} + 9x + 20 = 0

( x + 4 ) ( x + 5 ) = 0

Either x + 4 = 0 or x + 5 = 0

If x + 4 + 0

x = –4

If x + 5 = 0

x = –5

x = –4 or –5

## Example Two - Solve using the Quadratic Formula

Use the quadratic formula to solve x^{2} + 9x + 20 = 0

**Answer:**

a = 1

b = 9

c = 20

x = | –9 ± √ | 9^{2} – (4 × 1 × 20) |

2 × 1 |

x = –4 or –5

## Example Three

Use the quadratic formula to solve x^{2} – 3x – 40 = 0

**Answer:**

a = 1

b = –3

c = –40

x = | +3 ± √ | (–3)^{2} + (4 × 1 × 40) |

2 × 1 |

x = –5 or 8

## Example Four

Use the quadratic formula to solve 3x^{2} – 11x + 6 = 0

**Answer:**

a = 3

b = –11

c = 6

x = | +11 ± √ | (–11)^{2} – (4 × 3 × 6) |

2 × 3 |

x = 4.2 or –0.5

## Questions - Solve using the Quadratic Formula

**Q1.** x^{2} – 8x + 7 = 0
**Q2.** x^{2} – 18x + 81 = 0
**Q3.** x^{2} + 3x = 0

**Answers:**
**A1.** x = 1 or 7
**A2.** x = 9
**A3.** x = 0 or –3