Solving 80x2+-28x+-86 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:
80x2+-28x+-86=0.

There are two real solutions: x = 1.2264870422407, and x = -0.87648704224065.

Here's how we found that solution:

You entered the following equation:
(1)           80x2+-28x+-86=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)           \(x=--28\pm\frac{\sqrt{-28^2-4*80*-86}}{2*80}\)

which simplifies to:
(4)           \(x=--28\pm\frac{\sqrt{784--27520}}{160}\)

Now, solving for x, we find two real solutions:
\(x=\frac{--28+168.2379267585}{160}\) = 1.2264870422407,
  and
\(x=\frac{--28-168.2379267585}{160}\) = -0.87648704224065,

Both of these solutions are real numbers.
These are the two solutions that will satisfy the quadratic equation 80x2+-28x+-86=0.






Notes

What is a quadratic equation? Any equation that takes the form:
ax2 + bx + c = 0.
\ In this equation, x is a variable which is not known, and a, b, and c are constants. The constants a and b are called coefficients. Additionally, it should be noted that a cannot equal to 0 in the equation ax2+bx+c=0. If a is equal to 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.

Finding a solution to a quadratic equation can seem challenging. However, there are a number of methods for solving quadratic equations. One of the most widely used is the quadratic formula. The quadratic formula is:


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. Rarely, both roots may be the same, producing one solution for x.

Quadratic equations are more than just mathematical chores we have to endure. 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 hope you find this quadratic equation solver useful. 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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