3(4x-1)8x=17

Solution for 3(4x-1)8x=17 equation:

3(4x-1)8x=17

We move all terms to the left:

3(4x-1)8x-(17)=0

We multiply parentheses

96x^2-24x-17=0

a = 96; b = -24; c = -17;
Δ = b2-4ac
Δ = -242-4·96·(-17)
Δ = 7104
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:

$\sqrt{\Delta}=\sqrt{7104}=\sqrt{64*111}=\sqrt{64}*\sqrt{111}=8\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{111}}{2*96}=\frac{24-8\sqrt{111}}{192}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{111}}{2*96}=\frac{24+8\sqrt{111}}{192}
$