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

You entered:

There are two real solutions: x = 0.62422813026934, and x = -1.6242281302693.

(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) \(x=-72\pm\frac{\sqrt{72^2-4*72*-73}}{2*72}\)

which simplifies to:

(4) \(x=-72\pm\frac{\sqrt{5184--21024}}{144}\)

\(x=\frac{-72+161.88885075878}{144}\) = 0.62422813026934,

and

\(x=\frac{-72-161.88885075878}{144}\) = -1.6242281302693,

Both of these solutions are real numbers.

These are the two solutions that will satisfy the quadratic equation

ax

where a, b, and c are constants. X is unknown. The constants a and b, are referred to as coefficients. Interestingly, a cannot be equal to 0 in the equation ax

Calculating a solution to a quadratic equation may appear daunting, because both x and x

Solving a quadratic equation will always result in 2 solutions for x. These solutions are called roots. These roots may both be real numbers or, they may both be complex numbers. Rarely, the two roots may be the same, producing one solution for x.

You may be asking yourself, "Why is this stuff so important?" Quadratic equations are needed to calculate answers to many real-world problems. For example, to calculate the path of an accelerating object would require the use of s quadratic equation.

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 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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