24x(24-x)=2592

Solution for 24x(24-x)=2592 equation:

24x(24-x)=2592

We move all terms to the left:

24x(24-x)-(2592)=0

We add all the numbers together, and all the variables

24x(-1x+24)-2592=0

We multiply parentheses

-24x^2+576x-2592=0

a = -24; b = 576; c = -2592;
Δ = b2-4ac
Δ = 5762-4·(-24)·(-2592)
Δ = 82944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{82944}=288$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(576)-288}{2*-24}=\frac{-864}{-48}
=+18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(576)+288}{2*-24}=\frac{-288}{-48}
=+6
$