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
Reset

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

A quadratic equation is an function that has the form:
ax2 + bx + c = 0,
where a, b, and c are constants. X is unknown. A and b are called coefficients. Also, it is worth mentioning that a cannot be zero.

Solving a quadratic equation may appear daunting, because both x and x2 are unknown. However, any quadratic equation can quickly be solved using the quadratic formula. 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, these two roots may be the same, meaning there will only be one solution for x.

You may be asking yourself, "Why is this stuff so important?" Quadratic equations are needed to compute answers in many real-world fields, including engineering, pharmacokinetics and architecture.

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 hope the explanations showing how you can solve the equation yourself are educational and helpful. 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.

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