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

### Notes

What is a quadratic equation? Any function that can be written in the form: ax

^{2} + bx + c = 0. In this equation, x is a variable which is not known. A, b, and c are constants. A and b are referred to as coefficients. Interestingly, a cannot be 0. Otherwise, the equation ceases to be a quadratic equation, and becomes a linear equation.

Solving a linear equation is rather basic. Solving a quadratic equation is less straightforward. 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. Rarely, both roots may equal each other, meaning there will only be one solution for x.

Quadratic equations are an important part of mathematics. Quadratic equations are needed to find answers to many real-world problems. For example, to calculate the path of an accelerating object would require the use of s quadratic equation.

As mentioned above, in the equation ax

^{2}+bx+c=0, a cannot be zero. If a were 0, then ax

^{2} = 0x

^{2} = 0 for any value of x, so our equation becomes 0 + bx + c = 0, which is the same as bx + c = 0, which is no longer a quadratic equation. In fact, bx + c = 0 is a linear equation, which is much simpler to solve than a quadratic equation.

We hope you find this quadratic equation calculator useful. We encourage you to try it with different values, and to read the explanation for how to reach your answer. 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.