(8x+2)(12x-2)=120

Solution for (8x+2)(12x-2)=120 equation:

(8x+2)(12x-2)=120

We move all terms to the left:

(8x+2)(12x-2)-(120)=0

We multiply parentheses ..

(+96x^2-16x+24x-4)-120=0

We get rid of parentheses

96x^2-16x+24x-4-120=0

We add all the numbers together, and all the variables

96x^2+8x-124=0

a = 96; b = 8; c = -124;
Δ = b2-4ac
Δ = 82-4·96·(-124)
Δ = 47680
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:

$\sqrt{\Delta}=\sqrt{47680}=\sqrt{64*745}=\sqrt{64}*\sqrt{745}=8\sqrt{745}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{745}}{2*96}=\frac{-8-8\sqrt{745}}{192}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{745}}{2*96}=\frac{-8+8\sqrt{745}}{192}
$