(8x-6)3x=2

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

(8x-6)3x=2

We move all terms to the left:

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

We multiply parentheses

24x^2-18x-2=0

a = 24; b = -18; c = -2;
Δ = b2-4ac
Δ = -182-4·24·(-2)
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{129}}{2*24}=\frac{18-2\sqrt{129}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{129}}{2*24}=\frac{18+2\sqrt{129}}{48}
$