2(3x-1)4x=7

Solution for 2(3x-1)4x=7 equation:

2(3x-1)4x=7

We move all terms to the left:

2(3x-1)4x-(7)=0

We multiply parentheses

24x^2-8x-7=0

a = 24; b = -8; c = -7;
Δ = b2-4ac
Δ = -82-4·24·(-7)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{46}}{2*24}=\frac{8-4\sqrt{46}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{46}}{2*24}=\frac{8+4\sqrt{46}}{48}
$