2(4x-4)3x=3

Solution for 2(4x-4)3x=3 equation:

2(4x-4)3x=3

We move all terms to the left:

2(4x-4)3x-(3)=0

We multiply parentheses

24x^2-24x-3=0

a = 24; b = -24; c = -3;
Δ = b2-4ac
Δ = -242-4·24·(-3)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{6}}{2*24}=\frac{24-12\sqrt{6}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{6}}{2*24}=\frac{24+12\sqrt{6}}{48}
$