(13x-8)4x+1=2

Solution for (13x-8)4x+1=2 equation:

(13x-8)4x+1=2

We move all terms to the left:

(13x-8)4x+1-(2)=0

We add all the numbers together, and all the variables

(13x-8)4x-1=0

We multiply parentheses

52x^2-32x-1=0

a = 52; b = -32; c = -1;
Δ = b2-4ac
Δ = -322-4·52·(-1)
Δ = 1232
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:

$\sqrt{\Delta}=\sqrt{1232}=\sqrt{16*77}=\sqrt{16}*\sqrt{77}=4\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{77}}{2*52}=\frac{32-4\sqrt{77}}{104}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{77}}{2*52}=\frac{32+4\sqrt{77}}{104}
$