For a triangle $ABC$ with side lengths $|BC| = a$ units, $|AC| = b$ units and $|AB| = c$ units,
$$2a^{2} = 2b^{2} + 2c^{2} + 3bc$$
is satisfied.
Let $m(\widehat{BAC}) = x$. What is the value of $\tan x$?
A) $-\frac{\sqrt{2}}{3}$
B) $-\frac{\sqrt{3}}{3}$
C) $-\frac{\sqrt{5}}{3}$
D) $-\frac{\sqrt{6}}{3}$
E) $-\frac{\sqrt{7}}{3}$