Quadratic Equation Calculator

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


Welcome to Quadratic-Equation-Calculator.com, a free quadratic equation solver and tutorial. To solve your quadratic equation, and to get a step-by-step explanation of how that solution is reached, type your values for a, b, and c in the boxes above.
Or, click here for a random example of how to solve a quadratic equation using the quadratic formula.
A quadratic equation is any equation of the form ax2+bx+c=0, where a, b, and c are constants, and x is an unknown. Specifically, it's the term x2 that makes an equation quadratic. The term "quadratic" comes from the Latin word for "square."
Quadratic equations are used in all branches of science. Real-world applications of quadratic equations are found in equations of motion, the pharmacokinetics of some drugs, and even business. The geometries of parabolic antennas and mirrors are defined by quadratic functions.
There are several ways to solve a quadratic equation. Our quadratic equation calculator uses the quadratic formula, and shows you step-by-step how you can solve your quadratic equation using the quadratic formula, too. The quadratic formula is further described here.
To solve a quadratic equation ax2+bx+c=0, you need to solve for x. It turns out that x always has 2 values, called "roots." These 2 values for x may both be real numbers, or they both be complex numbers. Under very special circumstances, the 2 roots may be the same number, in which case there is only one solution.
Give our quadratic equation solver a try. Plug in your values for a, b, and c into the spaces above, and click "SOLVE FOR X".

Or, click here for a random example.