# Quadratic Equation Solver

*If you have an equation of the form " ax^{2} + bx + c = 0", we can solve it for you. *

Just enter the values of a, b and c below

Just enter the values of a, b and c below

## Is it Quadratic?

Only if it can be put in the form * ax^{2} + bx + c = 0*, and

*is*

**a***not zero*.

The name comes from "quad" meaning square, as the variable is squared (in other words * x^{2}*).

These are all quadratic equations in disguise:

In disguise | In standard form | a, b and c |
---|---|---|

x^{2} = 3x -1 |
x^{2} - 3x + 1 = 0 |
a=1, b=-3, c=1 |

2(x^{2} - 2x) = 5 |
2x^{2} - 4x - 5 = 0 |
a=2, b=-4, c=-5 |

x(x-1) = 3 |
x^{2} - x - 3 = 0 |
a=1, b=-1, c=-3 |

5 + 1/x - 1/x^{2} = 0 |
5x^{2} + x - 1 = 0 |
a=5, b=1, c=-1 |

## How Does this Work?

The solution(s) to a quadratic equation can be calculated using the **Quadratic Formula**:

The "±" means you need to do a plus AND a minus, so there are normally TWO solutions !

The blue part (**b ^{2} - 4ac**) is called the "discriminant", because it can "discriminate" between the possible
types of answer. If it is positive, you will get two real solutions, if it is zero you get just ONE solution, and if it is negative you get

*complex*solutions.

Note: you can still access the old version here.