To solve this equation, we first simplify the left side by using the properties of exponents.

3^4 - 5x * 3^(2x+6) = 1/18

3^4 = 81

5x 3^(2x+6) = 5x 3^2 3^6 = 5x 9 * 729 = 6561x

Now, the equation becomes:

81 - 6561x = 1/18

Rearranging the equation:

6561x = 81 - 1/18

6561x = (1458 - 1) / 18

6561x = 1457 / 18

x = 1457 / (18 * 6561)

x = 1457 / 118098

x ≈ 0.012347

Therefore, the value of x that satisfies the equation is approximately 0.012347.