Solving 27x2+-94x+73 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:
27x2+-94x+73=0.

There are two real solutions: x = 2.3121203192793, and x = 1.1693611622022.

Here's how we found that solution:

You entered the following equation:
(1)           27x2+-94x+73=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)           \(x=--94\pm\frac{\sqrt{-94^2-4*27*73}}{2*27}\)

which simplifies to:
(4)           \(x=--94\pm\frac{\sqrt{8836-7884}}{54}\)

Now, solving for x, we find two real solutions:
\(x=\frac{--94+30.854497241083}{54}\) = 2.3121203192793,
  and
\(x=\frac{--94-30.854497241083}{54}\) = 1.1693611622022,

Both of these solutions are real numbers.
These are the two solutions that will satisfy the quadratic equation 27x2+-94x+73=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 any function that takes the form: ax2 + bx + c = 0, where x is an unknown, and a, b, and c are constants. A and b are referred to as coefficients. Further, a cannot be equal to zero. Otherwise, the equation ceases to be a quadratic equation, and becomes a linear equation.

In contrast to solving a linear equation, solving a quadratic equation requires some more advanced mathematics.. 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. The quadratic formula is:


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 be equal, meaning there will only be one solution for x.

Who cares? Why do we care about qudratic equations? Quadratic equations are needed to calculate answers in many real-world fields, including engineering, pharmacokinetics and architecture.

The quadratic formula has been known for centuries. Brahmagupta, a mathematician from India, first described the quadratic formula as a means to calculate solutions to quadratic equations in the 7th Century AD.

We hope you find this quadratic equation solver useful. 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.

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