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
Reset

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? A quadratic equation is an function that takes the form:
ax2 + bx + c = 0,
where x is unknown. A, b, and c are constants. A and b are referred to as coefficients. It is worth noting that a cannot equal 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.

In contrast to solving a linear equation, solving a quadratic equation requires a few more steps. Fortunately, any quadratic equation can always be solved using the quadratic formula. The quadratic formula is written:


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 equal each other, producing one solution for x.

There are many uses for quadratic equations. Quadratic equations are needed to compute answers to many real-world problems. For example, to compute 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 calculator 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 your interest in Quadratic-Equation-Calculator.com.

click here for a random example of a quadratic equation.