Quadratic Formula

Here we will discuss the famous math quadratic formula for solving quadratic equations. The quadratic formula is very useful and using the quadratic formula is probably the easiest way to solve any quadratic equations as we shall demonstrate soon. The quadratic formula allows you to solve any quadratic equations in the following form.

How to solve Quadratic equations?

Quadratic equations are presented in the form:

In another word, a, x squared, plus, b x, plus c equals zero AND a is not equal to zero where:

• a is the coefficient of x squared,
• b is the coefficient of x and
• c is a constant.

Any quadratic equations can be re arranged into this form. Once we have the quadratic equation in this form, the quadratic formula for calculating x is given by the following.

Quadratic formula

Since any quadratic equations has two solutions, x is given by:

• negative b plus the square root of b squared minus 4 times a times c all divided by 2 times a, and
• negative b minus the square root of b squared minus 4 times a times c all divided by 2 times a.

Now you can solve any quadratic equations. But, just to make sure that you can, we are going to do an example of how to solve a quadratic equation. Let's solve a simple quadratic equation below.

Example of solving quadratic equation

Now we can re arrange to equation so that it is in the form a, x squared, plus b x, plus c as follows:

Now you can see that   a = 1, b = -1 and c = -6.

So, plugging a, b, and c into the quadratic formula, we have:

In another word, x is either 3 or -2. That's it. Now you know how to solve a quadratic equation.