x^2-18+13x=180

Solution for x^2-18+13x=180 equation:

x^2-18+13x=180

We move all terms to the left:

x^2-18+13x-(180)=0

We add all the numbers together, and all the variables

x^2+13x-198=0

a = 1; b = 13; c = -198;
Δ = b2-4ac
Δ = 132-4·1·(-198)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-31}{2*1}=\frac{-44}{2}
=-22
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+31}{2*1}=\frac{18}{2}
=9
$