24x(24-x)=2880

Solution for 24x(24-x)=2880 equation:

24x(24-x)=2880

We move all terms to the left:

24x(24-x)-(2880)=0

We add all the numbers together, and all the variables

24x(-1x+24)-2880=0

We multiply parentheses

-24x^2+576x-2880=0

a = -24; b = 576; c = -2880;
Δ = b2-4ac
Δ = 5762-4·(-24)·(-2880)
Δ = 55296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{55296}=\sqrt{9216*6}=\sqrt{9216}*\sqrt{6}=96\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(576)-96\sqrt{6}}{2*-24}=\frac{-576-96\sqrt{6}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(576)+96\sqrt{6}}{2*-24}=\frac{-576+96\sqrt{6}}{-48}
$