We cannot write 8x^{2} + 16x − 51 > 3 (2x − 3) (x + 4) as this would be correct only if (2x − 3) (x + 4) is positive.

Therefore, transfer 3 to L.H.S. and rewrite as

Multiplying both sides by the square of the denominator, we get

Therefore, the inequality has the solution