\[ax^{2} - \left( 18 + 2a^{2} \right)x + 36a > 0\]
\[Нет\ решения\ при\ a < 0;\ \ \]
\[D = 0.\]
\[D = \left( 18 + 2a^{2} \right)^{2} - 4a \cdot 36a =\]
\[= 324 + 72a^{2} + 4a^{4} - 144a^{2} =\]
\[= 4a^{4} - 72a^{2} + 324 =\]
\[= \left( 2a^{2} - 18 \right)^{2} = 0\]
\[2a^{2} - 18 = 0\]
\[2a^{2} = 18\]
\[a^{2} = 9\]
\[\left\{ \begin{matrix} a^{2} = 9 \\ a < 0\ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} \left\lbrack \begin{matrix} a = 3\ \ \ \ \\ a = - 3 \\ \end{matrix} \right.\ \\ a < 0\ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow a = - 3\]
\[Ответ:\ при\ a = - 3.\ \]