(2x+8)(2x+12)-96=96

Solution for (2x+8)(2x+12)-96=96 equation:

(2x+8)(2x+12)-96=96

We move all terms to the left:

(2x+8)(2x+12)-96-(96)=0

We add all the numbers together, and all the variables

(2x+8)(2x+12)-192=0

We multiply parentheses ..

(+4x^2+24x+16x+96)-192=0

We get rid of parentheses

4x^2+24x+16x+96-192=0

We add all the numbers together, and all the variables

4x^2+40x-96=0

a = 4; b = 40; c = -96;
Δ = b2-4ac
Δ = 402-4·4·(-96)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-56}{2*4}=\frac{-96}{8}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+56}{2*4}=\frac{16}{8}
=2
$