Algebra ->  Algebra  -> Quadratic Equations and Parabolas -> Quadratic Equation      Log On

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Welcome to the quadratic equation section. It gives you not only the answers, but also the complete solution for your equation, so that you can understand better how to solve quadratic equations.

You can start by reading the introduction into quadratic equations and how to solve them.

Solve equations of form: ` ax2 + bx + c = 0 `. The solver also draws a graph.
Please enter values of a, b, and c:

 ``` x2 +- x +- = 0 ```

A quadratic equation is an equation that looks like this:

``````
ax2+bx+c = 0```, ```
where a, b, and c are numbers, called coefficients.

Example: `x2+3x+4 = 0`

You can think about a quadratic equation in terms of a graph of a quadratic function, which is called a parabola. The equation means that you have to find the points on the horizontal axis (x) where the graph intersects with the axis.

To solve a quadratic equation, you have to calculate a number called discriminant, usually denoted as d:

`d = b2-4ac`

Depending on the value of d, there are the folowing three possibilities:

1. Discriminant d is greater than zero. The equation has two solutions.

```x1,2 = -b ± sqrt( b2-4ac )
------------------
2a

```
2. Discriminant is zero. There is only one solution.

```x = -b/2a
```
3. Discriminant is less than zero. No solutions are defined.

Note: for those of you who study complex numbers, there is a complex solution. If you do not know what complex numbers are, skip this part.

*Note: For those of you who are inclined to verify this formula, here's how to arrive to it: try to convert a standard quadratic equation to form

```	(x+q)2-p
```