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

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

 a x2 + b x + c = 0
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You entered:
30x2+96x+-75=0.

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:
(2)

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

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,
and
$$x=\frac{-96-134.96666255042}{60}$$ = -3.8494443758404,

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

### Notes

An equation that can be written as bx+c=0 is called a linear equation. It has one unknown, x, and 2 constants, b and c. If this equation were also to include the square of x as an unknown, it would become a quadratic equation. A quadratic equation is an function that has the form: ax2 + bx + c = 0. In this equation, x is an unknown. A, b, and c are constants. A and b are referred to as coefficients. Further, a cannot be 0 in the equation ax2+bx+c=0. If a equals 0, then ax2=0, and the equation becomes 0+bx+c=0, or bx+c=0. The equation bx+c=0 is a linear equation, and not a quadratic equation.

Solving a linear equation is basic. Solving a quadratic equation is less simple. However, you have this handy-dandy quadratic equation solver. Acutally, quadratic equations can be always 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. Here is the quadratic formula:

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. Under extraordinary circumstances, both roots may equal each other, meaning there will only be one solution for x.

Quadratic equations have real-life applications. Quadratic equations are needed to find answers to many real-world problems. The contour of a parablolic mirror is one example of an application of quadratic equations.

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 Quadratic-Equation-Calculator.com.