2(x-6)(30-x)=96

Solution for 2(x-6)(30-x)=96 equation:

2(x-6)(30-x)=96

We move all terms to the left:

2(x-6)(30-x)-(96)=0

We add all the numbers together, and all the variables

2(x-6)(-1x+30)-96=0

We multiply parentheses ..

2(-1x^2+30x+6x-180)-96=0

We multiply parentheses

-2x^2+60x+12x-360-96=0

We add all the numbers together, and all the variables

-2x^2+72x-456=0

a = -2; b = 72; c = -456;
Δ = b2-4ac
Δ = 722-4·(-2)·(-456)
Δ = 1536
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:

$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-16\sqrt{6}}{2*-2}=\frac{-72-16\sqrt{6}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+16\sqrt{6}}{2*-2}=\frac{-72+16\sqrt{6}}{-4}
$