3(4x-7)8x=14

Solution for 3(4x-7)8x=14 equation:

3(4x-7)8x=14

We move all terms to the left:

3(4x-7)8x-(14)=0

We multiply parentheses

96x^2-168x-14=0

a = 96; b = -168; c = -14;
Δ = b2-4ac
Δ = -1682-4·96·(-14)
Δ = 33600
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:

$\sqrt{\Delta}=\sqrt{33600}=\sqrt{1600*21}=\sqrt{1600}*\sqrt{21}=40\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-40\sqrt{21}}{2*96}=\frac{168-40\sqrt{21}}{192}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+40\sqrt{21}}{2*96}=\frac{168+40\sqrt{21}}{192}
$