4x(6-x)=24

Solution for 4x(6-x)=24 equation:

4x(6-x)=24

We move all terms to the left:

4x(6-x)-(24)=0

We add all the numbers together, and all the variables

4x(-1x+6)-24=0

We multiply parentheses

-4x^2+24x-24=0

a = -4; b = 24; c = -24;
Δ = b2-4ac
Δ = 242-4·(-4)·(-24)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{3}}{2*-4}=\frac{-24-8\sqrt{3}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{3}}{2*-4}=\frac{-24+8\sqrt{3}}{-8}
$