X(27-x)=180

Solution for X(27-x)=180 equation:

X(27-X)=180

We move all terms to the left:

X(27-X)-(180)=0

We add all the numbers together, and all the variables

X(-1X+27)-180=0

We multiply parentheses

-1X^2+27X-180=0

a = -1; b = 27; c = -180;
Δ = b2-4ac
Δ = 272-4·(-1)·(-180)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3}{2*-1}=\frac{-30}{-2}
=+15
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3}{2*-1}=\frac{-24}{-2}
=+12
$