\[\left( a^{2} - 6a - 27 \right)x =\]
\[= 3a² + 10a + 3\]
\[x = \frac{3a^{2} + 10a + 3}{a^{2} - 6a - 27} =\]
\[3a^{2} + 10a + 3 = 0\]
\[D_{1} = 25 - 9 = 16\]
\[a_{1} = \frac{- 5 + 4}{3} = - \frac{1}{3};\ \ \ \ \]
\[a_{2} = \frac{- 5 - 4}{3} = - 3.\]
\[3a^{2} + 10a + 3 =\]
\[= 3 \cdot \left( a + \frac{1}{3} \right)(a + 3) =\]
\[= (3a + 1)(a + 3).\]
\[a^{2} - 6a - 27 = 0\]
\[a_{1} + a_{2} = 6;\ \ a_{1} \cdot a_{2} = - 27\]
\[a_{1} = 9;\ \ \ \ a_{2} = - 3\]
\[a^{2} - 6a - 27 = (a - 9)(a + 3).\]
\[1)\ \ a = - 3:\]
\[\left( ( - 3)^{2} - 6 \cdot ( - 3) - 27 \right) \cdot x =\]
\[= 3 \cdot ( - 3)^{2} + 10 \cdot ( - 3) + 3.\]
\[0 \cdot x = 0\]
\[x - любое\ число.\]
\[2)\ \ a = 9:\]
\[нет\ решения.\]
\[3)\ \ a = - \frac{1}{3}:\]
\[x = 0.\]
\[4)\ \ a \neq - 3,\ a \neq 9,\ a \neq - \frac{1}{3}:\]
\[x = \frac{3a + 1}{a - 9}.\]