(2+3x)64x=180

Solution for (2+3x)64x=180 equation:

(2+3x)64x=180

We move all terms to the left:

(2+3x)64x-(180)=0

We add all the numbers together, and all the variables

(3x+2)64x-180=0

We multiply parentheses

192x^2+128x-180=0

a = 192; b = 128; c = -180;
Δ = b2-4ac
Δ = 1282-4·192·(-180)
Δ = 154624
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:

$\sqrt{\Delta}=\sqrt{154624}=\sqrt{1024*151}=\sqrt{1024}*\sqrt{151}=32\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-32\sqrt{151}}{2*192}=\frac{-128-32\sqrt{151}}{384}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+32\sqrt{151}}{2*192}=\frac{-128+32\sqrt{151}}{384}
$