Yet another question 5

Let a quadratic equation be represented as

$A(\sqrt{3} - \sqrt{2})x^2 + \dfrac {Bx}{(\sqrt{3} + \sqrt{2})} + C=0,$

where $A = (49 + 20\sqrt 6)^{1/4}$ and $B= 8\sqrt 3 + \dfrac{8\sqrt6}{\sqrt 3} + \dfrac{16}{\sqrt3} + ....$.

Let $\alpha$ and $\beta$ be the roots of the above equation which are related to the constraint $( \displaystyle | \alpha - \beta | = (6\sqrt6)^k,$

where $\displaystyle k = \log_{6}10 - 2\log_6 \sqrt5 + \log_6\sqrt{\log_{6} 18 + \log_{6} 72}$.

Find the value of $C$.