I have the feeling that something is missing in there. You got that by clearing denominators and simplifying, right

 Multiplying the whole equation by $4x^2(x^2+3)$, we have $4(x^2+3)-4x^2 = 3(x^2)(x^2+3)$, so $12 = 3(x^2)^2 + 9(x^2)$. Try solving first for $x^2$, and then for $x$ from there.