To solve this equation, we first need to simplify both sides by finding a common denominator.

(3-4x)/3 - (8+9x)/4 = (9-4x)/8

First, multiply the first fraction by 4/4 and the second fraction by 3/3 to get a common denominator of 12:

(4(3-4x)/12) - (3(8+9x)/12) = (9-4x)/8

Simplify:

(12 - 16x - 24 - 27x)/12 = (9-4x)/8

Combine like terms:

(-15 - 43x)/12 = (9-4x)/8

Cross multiply to eliminate fractions:

8(-15 - 43x) = 12(9-4x)

-120 - 344x = 108 - 48x

Add 48x to both sides:

-120 - 296x = 108

Add 120 to both sides:

-296x = 228

Divide by -296:

x = -57/37

So the solution to the equation is x = -57/37.