A free quadratic equation calculator that shows and explains each step in solving your quadratic equation.

- Example #1: Solving A Quadratic Equation with 2 Real Solutions
- Example #2: Solving A Quadratic Equation with 2 Complex Solutions
- click here for a random example.

Let's take the equation **4r**^{2} + 8r + 1 = 0.

So let's plug the values for**a**, **b**, and **c** into our quadratic equation solver like so:

Now, click "solve for X," and let's see what happens.

So let's plug the values for

Let's take the equation **8r**^{2} = -2r - 1.

Wait! This looks different than our other equations! But, not to worry, it's still a quadratic equation. Let's just rearrange it into this form

(1)**8r**^{2} + 2r = -1,

which can be further rearranged to look like this:

(2)**8r**^{2} + 2r + 1 = 0.

Now, it doesn't matter if our variable is named**r** or **x** or **whatever**. It is a variable, and we're solving for it's value.

So let's plug the values for**a**, **b**, and **c** into our quadratic equation solver like so:

Now, click "solve for X," and let's see what happens.

Wait! This looks different than our other equations! But, not to worry, it's still a quadratic equation. Let's just rearrange it into this form

(1)

which can be further rearranged to look like this:

(2)

Now, it doesn't matter if our variable is named

So let's plug the values for