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 has the form: ax

^{2} + bx + c = 0, where a, b, and c are constants. X is a variable which is not known. The constants a and b, are referred to as coefficients. Also, a cannot equal to 0. Otherwise, the equation ceases to be a quadratic equation, and becomes a linear equation.

Solving a quadratic equation may appear daunting, because both x and x

^{2} are unknown. However, you have this handy-dandy quadratic equation calculator. All kidding aside, quadratic equations can be quickly 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. 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. Depending on the values of a, b, and c, these two roots may equal each other, producing one solution for x.

Quadratic equations are important. Quadratic equations are needed to find answers in many real-world fields, including physics, pharmacokinetics and architecture.

Because equations can be rearranged without losing their meaning, sometimes you may see an equation that isn't written exactly this way, but it's still a quadratic equation. For example, you probably know that

ax

^{2} + bx + c = 0 means exactly the same thing as 0 = c + bx + ax

^{2}. They're just written differently.

Here are some other examples of ways to write the quadratic equation. They all mean the same thing:

(1) \(ax^2+bx=d\), where d = -c

(2) \(x^2+bx-d=e\), where a=1 and d=e-c

(3) \(ax^2=ex+d\), where d=-c and e=-b

(4) \(\frac{x^2}{f}-d=ex\), where d=-c and e=-b and \(f=\frac{1}{a}\)

Look at each of the examples above. Do you understand why they are still quadratic equations, and how they can be rearranged to look like our familiar formula?

We this quadratic equation calculator is useful to you. 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 using Quadratic-Equation-Calculator.com.

click here for a random example of a quadratic equation.