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:

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

What is a quadratic equation? A quadratic equation is an function that can be written as: ax2 + bx + c = 0. In this equation, x is a variable which is not known. A, b, and c are constants. A and b are referred to as coefficients. Interestingly, a cannot equal to zero in the equation ax2+bx+c=0. Otherwise, the equation ceases to be a quadratic equation, and becomes a linear equation.

Solving a linear equation is pretty simple. Solving a quadratic equation is more complicated. Fortunately, you have this handy-dandy quadratic equation solver. All kidding aside, 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. This is the quadratic formula:


When you compute a solution to a quadratic equation, you will always find 2 values for x, 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.

There are many uses for quadratic equations. Quadratic equations are needed to calculate answers in many real-world fields, including physics, 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 solver 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 using Quadratic-Equation-Calculator.com.

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