4(3x-1)2x=86

Solution for 4(3x-1)2x=86 equation:

4(3x-1)2x=86

We move all terms to the left:

4(3x-1)2x-(86)=0

We multiply parentheses

24x^2-8x-86=0

a = 24; b = -8; c = -86;
Δ = b2-4ac
Δ = -82-4·24·(-86)
Δ = 8320
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:

$\sqrt{\Delta}=\sqrt{8320}=\sqrt{64*130}=\sqrt{64}*\sqrt{130}=8\sqrt{130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{130}}{2*24}=\frac{8-8\sqrt{130}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{130}}{2*24}=\frac{8+8\sqrt{130}}{48}
$