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

You entered:

There are two real solutions: x = -1.4545454545455, and x = -3.

(1)

For any quadratic equation

(2)

In the form above, you specified values for the variables a, b, and c. Plugging those values into Eqn. 1, we get:

(3) \(x=-98\pm\frac{\sqrt{98^2-4*22*96}}{2*22}\)

which simplifies to:

(4) \(x=-98\pm\frac{\sqrt{9604-8448}}{44}\)

\(x=\frac{-98+34}{44}\) = -1.4545454545455,

and

\(x=\frac{-98-34}{44}\) = -3,

Both of these solutions are real numbers.

These are the two solutions that will satisfy the quadratic equation

Solving a linear equation is rather simple. Solving a quadratic equation requires some more advanced mathematics. Fortunately, 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. The quadratic formula is:

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, both roots may be the same, producing one solution for x.

Quadratic equations have real-life applications. Quadratic equations are needed to calculate answers in many real-world fields, including physics, biology and business.

In our equation, a cannot be zero. However, b can be zero, and so can c.

We hope you find this quadratic equation solver 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.

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