Solving 30x2+96x+-75 using the Quadratic Formula

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

For your equation of the form "ax2 + bx + c = 0," enter the values for a, b, and c:

= 0

You entered:

There are two real solutions: x = 0.6494443758404, and x = -3.8494443758404.

Here's how we found that solution:

You entered the following equation:
(1)           30x2+96x+-75=0.

For any quadratic equation ax2 + bx + c = 0, one can solve for x using the following equation, which is known as the quadratic formula:

In the form above, you specified values for the variables a, b, and c. Plugging those values into Eqn. 1, we get:
(3)           \(x=-96\pm\frac{\sqrt{96^2-4*30*-75}}{2*30}\)

which simplifies to:
(4)           \(x=-96\pm\frac{\sqrt{9216--9000}}{60}\)

Now, solving for x, we find two real solutions:
\(x=\frac{-96+134.96666255042}{60}\) = 0.6494443758404,
\(x=\frac{-96-134.96666255042}{60}\) = -3.8494443758404,

Both of these solutions are real numbers.
These are the two solutions that will satisfy the quadratic equation 30x2+96x+-75=0.


What is a quadratic equation? A quadratic equation is an function that takes the form: ax2 + bx + c = 0, where x is a variable of unknown value. A, b, and c are constants. A and b are called coefficients. Furthermore, it should be mentioned that a cannot be 0 in the equation ax2+bx+c=0.

Solving a quadratic equation may appear daunting, because both x and x2 are unknown. Fortunately, any quadratic equation can reliably be solved using the quadratic formula. Here 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, the two roots may equal each other, resulting in one solution for x.

Why do we care about qudratic equations? Quadratic equations are needed to compute answers in many real-world fields, including engineering, biology and business.

As mentioned above, in the equation ax2+bx+c=0, a cannot be zero. If a were 0, then ax2 = 0x2 = 0 for any value of x, so our equation becomes 0 + bx + c = 0, which is the same as bx + c = 0, which is no longer a quadratic equation. In fact, bx + c = 0 is a linear equation, which is much simpler to solve than a quadratic equation.

We this quadratic equation calculator 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 using

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