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

### Notes

What is a quadratic equation? A quadratic equation is an function that can be written as: 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 equal to zero in the equation ax

^{2}+bx+c=0. Otherwise, the equation ceases to be a quadratic equation, and becomes a linear equation.

Solving a linear equation is pretty simple. Solving a quadratic equation is more complicated. Fortunately, you have this handy-dandy quadratic equation solver. All kidding aside, quadratic equations can be always solved using the

quadratic formula, which is the same technique used by this quadratic equation solver. Try it, and it will explain each of the steps to you. This 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. Under extraordinary circumstances, both roots may equal each other, meaning there will only be one solution for x.

There are many uses for quadratic equations. Quadratic equations are needed to calculate answers in many real-world fields, including physics, biology and business.

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 this quadratic equation solver is useful to you. We encourage you to plug in different values for a, b, and c. But, if you just want to use it to calculate the answers to your quadratic equations, that's cool too. Thank you for using Quadratic-Equation-Calculator.com.

click here for a random example of a quadratic equation.