3(2x-8)4x=26

Solution for 3(2x-8)4x=26 equation:

3(2x-8)4x=26

We move all terms to the left:

3(2x-8)4x-(26)=0

We multiply parentheses

24x^2-96x-26=0

a = 24; b = -96; c = -26;
Δ = b2-4ac
Δ = -962-4·24·(-26)
Δ = 11712
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:

$\sqrt{\Delta}=\sqrt{11712}=\sqrt{64*183}=\sqrt{64}*\sqrt{183}=8\sqrt{183}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-8\sqrt{183}}{2*24}=\frac{96-8\sqrt{183}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+8\sqrt{183}}{2*24}=\frac{96+8\sqrt{183}}{48}
$