X+x(x-18)=180

Solution for X+x(x-18)=180 equation:

X+X(X-18)=180

We move all terms to the left:

X+X(X-18)-(180)=0

We multiply parentheses

X^2+X-18X-180=0

We add all the numbers together, and all the variables

X^2-17X-180=0

a = 1; b = -17; c = -180;
Δ = b2-4ac
Δ = -172-4·1·(-180)
Δ = 1009
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{1009}}{2*1}=\frac{17-\sqrt{1009}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{1009}}{2*1}=\frac{17+\sqrt{1009}}{2}
$