2(3x+12)6x=8

Solution for 2(3x+12)6x=8 equation:

2(3x+12)6x=8

We move all terms to the left:

2(3x+12)6x-(8)=0

We multiply parentheses

36x^2+144x-8=0

a = 36; b = 144; c = -8;
Δ = b2-4ac
Δ = 1442-4·36·(-8)
Δ = 21888
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:

$\sqrt{\Delta}=\sqrt{21888}=\sqrt{576*38}=\sqrt{576}*\sqrt{38}=24\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-24\sqrt{38}}{2*36}=\frac{-144-24\sqrt{38}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+24\sqrt{38}}{2*36}=\frac{-144+24\sqrt{38}}{72}
$