Help would be appreciated
I assume that you wanted $\displaystyle X$ and $\displaystyle x$ to be the same thing, and that you wanted to solve this equation for $\displaystyle x$.
$\displaystyle x^2 + x\log{6} + (\log{2})(\log{3}) = 0$
This is a Quadratic of the form $\displaystyle ax^2 + bx + c = 0$, so the roots are $\displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.