(3x+1)8x=640

Solution for (3x+1)8x=640 equation:

(3x+1)8x=640

We move all terms to the left:

(3x+1)8x-(640)=0

We multiply parentheses

24x^2+8x-640=0

a = 24; b = 8; c = -640;
Δ = b2-4ac
Δ = 82-4·24·(-640)
Δ = 61504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{61504}=248$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-248}{2*24}=\frac{-256}{48}
=-5+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+248}{2*24}=\frac{240}{48}
=5
$