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

You entered:

There are no solutions in the real number domain.

There are two complex solutions: x = -1.2638888888889 + 0.6970783384072

where

(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) \(x=-91\pm\frac{\sqrt{91^2-4*36*75}}{2*36}\)

which simplifies to:

(4) \(x=-91\pm\frac{\sqrt{8281-10800}}{72}\)

(5) \(x=-91\pm\frac{\sqrt{-2519}}{72}\)

This means that our solution will require finding the square root of a negative number. There is no real number solution for this, so our solution will be a complex number (that is, it will involve the imaginary number

Let's calculate the square root:

(6) \(x=-91\pm\frac{50.189640365318i}{72}\)

This equation further simplifies to:

(7) \(x=-\frac{-91}{72}\pm0.6970783384072i\)

Solving for x, we find two solutions which are both complex numbers:

x = -1.2638888888889 + 0.6970783384072

and

x = -1.2638888888889 - 0.6970783384072

Both of these solutions are complex numbers.

These are the two solutions that will satisfy the equation

In contrast to solving a linear equation, solving a quadratic equation is a more complicated task. Fortunately, you have this handy-dandy quadratic equation solver. Acutally, quadratic equations can be quickly 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:

Since there are always 2 solutions to a square root (one negative, one positive), solving the quadratic equation results in 2 values for x. The two solutions for x (which may be positive or negative, real or complex) are called roots. Rarely, these two roots may equal each other, resulting in one solution for x.

Quadratic equations are important. Quadratic equations are needed to compute answers in many real-world fields, including engineering, biology and business.

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

We this quadratic equation solver 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, if you just want to use it to calculate the answers to your quadratic equations, that's cool too. Thank you for your interest in Quadratic-Equation-Calculator.com.

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