2(3x-1)2x=14

Solution for 2(3x-1)2x=14 equation:

2(3x-1)2x=14

We move all terms to the left:

2(3x-1)2x-(14)=0

We multiply parentheses

12x^2-4x-14=0

a = 12; b = -4; c = -14;
Δ = b2-4ac
Δ = -42-4·12·(-14)
Δ = 688
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:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{43}}{2*12}=\frac{4-4\sqrt{43}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{43}}{2*12}=\frac{4+4\sqrt{43}}{24}
$