X(11+x)=180

Solution for X(11+x)=180 equation:

X(11+X)=180

We move all terms to the left:

X(11+X)-(180)=0

We add all the numbers together, and all the variables

X(X+11)-180=0

We multiply parentheses

X^2+11X-180=0

a = 1; b = 11; c = -180;
Δ = b2-4ac
Δ = 112-4·1·(-180)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-29}{2*1}=\frac{-40}{2}
=-20
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+29}{2*1}=\frac{18}{2}
=9
$