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

You entered:

There are two real solutions: x = 2.3121203192793, and x = 1.1693611622022.

(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) \(x=--94\pm\frac{\sqrt{-94^2-4*27*73}}{2*27}\)

which simplifies to:

(4) \(x=--94\pm\frac{\sqrt{8836-7884}}{54}\)

\(x=\frac{--94+30.854497241083}{54}\) = 2.3121203192793,

and

\(x=\frac{--94-30.854497241083}{54}\) = 1.1693611622022,

Both of these solutions are real numbers.

These are the two solutions that will satisfy the quadratic equation

In contrast to solving a linear equation, solving a quadratic equation is a more complicated task. However, you have this handy-dandy quadratic equation solver. Acutally, quadratic equations can be readily 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. The quadratic formula is written:

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 have the same value, producing one solution for x.

Why do we need to be able to solve quadratic equations? Quadratic equations are needed to compute answers in many real-world fields, including physics, pharmacokinetics and business.

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 solver is useful to you. We hope the explanations showing how you can solve the equation yourself are educational and helpful. 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.

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