As written you will get a third order polynomial like this:
0 = 8X^3 + 16X^2 -9X +4 by multiplying every term on both sides by the Lowest Common Multiple which is 2X(X+2). The LCM is every denominator factor raised to the highest power you find for that factor. You'll then need to solve this polynomial by synthetic division or use a root solver routine on a calculator like PolySim for the TI 83 plus or TI 84. If one of the roots is imaginary, its conjugate is also a root. There will be 3 roots.
This works because the denominator under the 9 factors to X(X + 2) and multiplying by this LCM clears all of the denominators.
I wonder if the 4X + 9 is really like this (4X + 9). If so... clearing the denominator as described gives you:
7X +14 +2X = 8X + 18 and that leads to a nice solution of X = 4
Let me know if this last interpretation is the correct one.