Solve: 6x^4 - 10x^2 - 12 > 10x^3 + 38x

where x is a member of the real numbers.

I rearranged it as an equality equaling zero, as:

6x^4 - 10x^3 - 10x^2 - 38x - 12 = 0

I then factored out a 2, giving:

(2)(3x^4 - 5x^3 - 5x^2 -19x - 6) = 0

Using factor theorum and synthetic division, I determined that:

(2)(3)(x + 1/3)(x - 3)(x^2 + x + 2) = 0

However, the quadratic equation above does not yield any real solutions (unless I'm doing it wrong). Where do I go from here?