3(x-4)8x=13

Solution for 3(x-4)8x=13 equation:

3(x-4)8x=13

We move all terms to the left:

3(x-4)8x-(13)=0

We multiply parentheses

24x^2-96x-13=0

a = 24; b = -96; c = -13;
Δ = b2-4ac
Δ = -962-4·24·(-13)
Δ = 10464
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:

$\sqrt{\Delta}=\sqrt{10464}=\sqrt{16*654}=\sqrt{16}*\sqrt{654}=4\sqrt{654}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-4\sqrt{654}}{2*24}=\frac{96-4\sqrt{654}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+4\sqrt{654}}{2*24}=\frac{96+4\sqrt{654}}{48}
$