108=(24-x)x

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

108=(24-x)x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -((-1x+24)x), so:

(-1x+24)x

We multiply parentheses

-1x^2+24x

Back to the equation:

-(-1x^2+24x)


We get rid of parentheses

1x^2-24x+108=0

We add all the numbers together, and all the variables

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