(2x-117)+x^2=180

Solution for (2x-117)+x^2=180 equation:

(2x-117)+x^2=180

We move all terms to the left:

(2x-117)+x^2-(180)=0

We get rid of parentheses

x^2+2x-117-180=0

We add all the numbers together, and all the variables

x^2+2x-297=0

a = 1; b = 2; c = -297;
Δ = b2-4ac
Δ = 22-4·1·(-297)
Δ = 1192
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1192}=\sqrt{4*298}=\sqrt{4}*\sqrt{298}=2\sqrt{298}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{298}}{2*1}=\frac{-2-2\sqrt{298}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{298}}{2*1}=\frac{-2+2\sqrt{298}}{2}
$