4(3d-2)8d=5

Solution for 4(3d-2)8d=5 equation:

4(3d-2)8d=5

We move all terms to the left:

4(3d-2)8d-(5)=0

We multiply parentheses

96d^2-64d-5=0

a = 96; b = -64; c = -5;
Δ = b2-4ac
Δ = -642-4·96·(-5)
Δ = 6016
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6016}=\sqrt{64*94}=\sqrt{64}*\sqrt{94}=8\sqrt{94}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-8\sqrt{94}}{2*96}=\frac{64-8\sqrt{94}}{192}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+8\sqrt{94}}{2*96}=\frac{64+8\sqrt{94}}{192}
$