x(36-3x)=96

Solution for x(36-3x)=96 equation:

x(36-3x)=96

We move all terms to the left:

x(36-3x)-(96)=0

We add all the numbers together, and all the variables

x(-3x+36)-96=0

We multiply parentheses

-3x^2+36x-96=0

a = -3; b = 36; c = -96;
Δ = b2-4ac
Δ = 362-4·(-3)·(-96)
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{-(36)-12}{2*-3}=\frac{-48}{-6}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12}{2*-3}=\frac{-24}{-6}
=+4
$