# Quadratic Equation Solver

*We can help you solve an equation of the form " ax^{2} + bx + c = 0"*

*:*

Just enter the values of a, b and c below

Just enter the values of a, b and c below

algebra/images/quadratic-solver.js

## 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 we 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:

- when it is positive, we get two real solutions,
- when it is zero we get just ONE solution,
- when it is negative we get
*complex*solutions.

Learn more at Quadratic Equations