2(x+6)3x=8

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

2(x+6)3x=8

We move all terms to the left:

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

We multiply parentheses

6x^2+36x-8=0

a = 6; b = 36; c = -8;
Δ = b2-4ac
Δ = 362-4·6·(-8)
Δ = 1488
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:

$\sqrt{\Delta}=\sqrt{1488}=\sqrt{16*93}=\sqrt{16}*\sqrt{93}=4\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{93}}{2*6}=\frac{-36-4\sqrt{93}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{93}}{2*6}=\frac{-36+4\sqrt{93}}{12}
$