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

### Notes

What is a quadratic equation? Any equation that can take the form: ax

^{2} + bx + c = 0, where x is an unknown. A, b, and c are constants. A and b are referred to as coefficients. Further, it is worth mentioning that a cannot be equal to zero in the equation ax

^{2}+bx+c=0. If a=0, then ax

^{2}=0, and the equation becomes 0+bx+c=0, or bx+c=0. The equation bx+c=0 is a linear equation, and not a quadratic equation.

Solving a linear equation is straightforward. Solving a quadratic equation is less straightforward. However, any quadratic equation can quickly be solved using the

quadratic formula. Here is the quadratic formula:

Solving a quadratic equation will always result in 2 solutions for x. These solutions are called roots. These roots may both be real numbers or, they may both be complex numbers. Rarely, the two roots may have the same value, producing one solution for x.

Quadratic equations are more than just mathematical flights of fantasy Quadratic equations are needed to compute answers to many real-world problems. The contour of a parablolic dish antenna is one example of an application of quadratic equations.

The term "quadratic" comes from the Latin word

*quadratum,* which means "square." Why? Because what defines a quadratic equation is the inclusion of some variable squared. In our equation above, the term x

^{2} (x squared) is what makes this equation quadratic.

We hope you find this quadratic equation solver useful. We hope the explanations showing how you can solve the equation yourself are educational and helpful. But we totally understand if you just want to use it to find the answers you're looking for. Thank you for your interest in Quadratic-Equation-Calculator.com.

click here for a random example of a quadratic equation.