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

You entered:

There are two real solutions: x = 0.57692307692308, and x = -1.6666666666667.

(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) \(x=-85\pm\frac{\sqrt{85^2-4*78*-75}}{2*78}\)

which simplifies to:

(4) \(x=-85\pm\frac{\sqrt{7225--23400}}{156}\)

\(x=\frac{-85+175}{156}\) = 0.57692307692308,

and

\(x=\frac{-85-175}{156}\) = -1.6666666666667,

Both of these solutions are real numbers.

These are the two solutions that will satisfy the quadratic equation

Solving a linear equation is fairly simple. Solving a quadratic equation requires more work. Fortunately, any quadratic equation can reliably be solved using the quadratic formula. 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. Depending on the values of a, b, and c, both roots may be equal, producing one solution for x.

Quadratic equations are an important part of mathematics. Quadratic equations are needed to find answers to many real-world problems. For example, to calculate whether a braking car can stop fast enough to avoid hitting something would require the use of s quadratic equation.

The term "quadratic" comes from the Latin word

We this quadratic equation calculator 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 your interest in Quadratic-Equation-Calculator.com.

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