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

### Notes

What is a quadratic equation? Any equation ax

^{2} + bx + c = 0, where x is a variable which is not known, and a, b, and c are constants. A and b are referred to as coefficients. Further, a cannot equal to 0. If a is 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.

Calculating a solution to a quadratic equation may appear daunting, because both x and x

^{2} are unknown. Fortunately, you have this handy-dandy quadratic equation calculator. All kidding aside, quadratic equations can be reliably solved using the

quadratic formula, which is the same technique used by this quadratic equation calculator. Try it, and it will explain each of the steps to you. Here is the quadratic formula:

When you compute a solution to a quadratic equation, you will always find 2 values for x, called "roots". These roots may both be real numbers or, they may both be complex numbers. Depending on the values of a, b, and c, these two roots may equal each other, producing one solution for x.

Quadratic equations are an important part of mathematics. Quadratic equations are needed to find answers in many real-world fields, including engineering, pharmacokinetics and architecture.

The quadratic formula has been known for centuries. Brahmagupta, a mathematician from India, first described the quadratic formula as a means to calculate solutions to quadratic equations in the 7th Century AD.

We this quadratic equation calculator is useful to you. We encourage you to plug in different values for a, b, and c. 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.