X(24-x)=108

Solution for X(24-x)=108 equation:

X(24-X)=108

We move all terms to the left:

X(24-X)-(108)=0

We add all the numbers together, and all the variables

X(-1X+24)-108=0

We multiply parentheses

-1X^2+24X-108=0

a = -1; b = 24; c = -108;
Δ = b2-4ac
Δ = 242-4·(-1)·(-108)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12}{2*-1}=\frac{-36}{-2}
=+18
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12}{2*-1}=\frac{-12}{-2}
=+6
$