\[\frac{3a^{2} - 11a - 4}{a^{2} - 16} = \frac{(3a + 1)(a - 4)}{(a - 4)(a + 4)} = \frac{3a + 1}{a + 4}\]
\[3a^{2} - 11a - 4 = 3 \cdot \left( a + \frac{1}{3} \right)(a - 4) =\]
\[= (3a + 1)(a - 4)\]
\[D = 121 + 48 = 169\]
\[a_{1} = \frac{11 + 13}{6} = 4;\]
\[a_{2} = \frac{11 - 13}{6} = - \frac{2}{6} = - \frac{1}{3}.\]