Expanding the left side of the equation, we get:

(3x+4)^2 = (3x+4)(3x+4) = 9x^2 + 12x + 12x + 16 = 9x^2 + 24x + 16

Expanding the right side of the equation, we get:

(3x+1)(3x-1) = 9x^2 - 3x + 3x - 1 = 9x^2 - 1

Now, substituting the expanded forms back into the original equation, we have:

9x^2 + 24x + 16 - (9x^2 - 1) = 49
9x^2 + 24x + 16 - 9x^2 + 1 = 49
24x + 17 = 49
24x = 32
x = 32/24
x = 4/3

Therefore, the solution to the equation is x = 4/3.