How to find the coefficient of $a$ in a quadratic equation? 
If a root of the equation $$3x^2 + 4x + 12a + 9ax = 0$$ is greater than 6, then the correct statement of the coefficient $a$ is:
a) $a = 2$
b) $a> -2$
c) $a = -2$
d) $a <-2$
e) $-2\le a\le 2$

What I did was solve it as if a root was exactly $6$, and I find that $a$ is equal to $2$ ... But the premise says that a root has to be greater than $6$, not equal to $6$ ... and I do not know how find that, for now I would know that $a$ does not have to be $2$ ...

Using @dxiv hint $(x+3a)(3x+4) = 0$ we have $x = -\frac{4}{3} < 6$ and $x = -3a > 6$ Therefore, $a < -2$
