(2x+12)(2x+8)-12(8)=300

Solution for (2x+12)(2x+8)-12(8)=300 equation:

(2x+12)(2x+8)-12(8)=300

We move all terms to the left:

(2x+12)(2x+8)-12(8)-(300)=0

We add all the numbers together, and all the variables

(2x+12)(2x+8)-428=0

We multiply parentheses ..

(+4x^2+16x+24x+96)-428=0

We get rid of parentheses

4x^2+16x+24x+96-428=0

We add all the numbers together, and all the variables

4x^2+40x-332=0

a = 4; b = 40; c = -332;
Δ = b2-4ac
Δ = 402-4·4·(-332)
Δ = 6912
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:

$\sqrt{\Delta}=\sqrt{6912}=\sqrt{2304*3}=\sqrt{2304}*\sqrt{3}=48\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-48\sqrt{3}}{2*4}=\frac{-40-48\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+48\sqrt{3}}{2*4}=\frac{-40+48\sqrt{3}}{8}
$