(24-x)x=108

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

(24-x)x=108

We move all terms to the left:

(24-x)x-(108)=0

We add all the numbers together, and all the variables

(-1x+24)x-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
$