Examples of How to Solve a Quadratic Equation

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


For your equation of the form "ax2 + bx + c = 0," enter the values for a, b, and c:

a
 
x2
 
+
b
 
x
 
+
c
 
= 0


Examples


Example #1: Solving A Quadratic Equation with 2 Real Solutions

Let's take the equation 4r2 + 8r + 1 = 0.
So let's plug the values for a, b, and c into our quadratic equation solver like so:
For your equation of the form "ax2 + bx + c = 0," enter the values for a, b, and c:
a
 
x2
 
+
b
 
x
 
+
c
 
= 0

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


Example #2: Solving A Quadratic Equation with 2 Complex Solutions

Let's take the equation 8r2 = -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) 8r2 + 2r = -1,
which can be further rearranged to look like this:
(2) 8r2 + 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:
For your equation of the form "ax2 + bx + c = 0," enter the values for a, b, and c:
a
 
x2
 
+
b
 
x
 
+
c
 
= 0

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