При каждом значении параметра k решите уравнение: x^2-(3k-3)x-9k=0.

\[x^{2} - (3k - 3)x - 9k = 0\]

\[D = (3k - 3)^{2} - 4 \bullet ( - 9k) =\]

\[= 9k^{2} - 18k + 9 + 36k =\]

\[= 9k^{2} + 18k + 9 =\]

\[= 9 \bullet \left( k^{2} + 2k + 1 \right) =\]

\[= 9{\bullet (k + 1)}^{2}\]

\[k \neq - 1 \Longrightarrow D > 0 \Longrightarrow\]

\[x_{1} = \frac{3k - 3 + 3 \bullet (k + 1)}{2} =\]

\[= \frac{3k - 3 + 3k + 3}{2} = 3k\]

\[x_{2} = \frac{3k - 3 - 3 \bullet (k + 1)}{2} =\]

\[= \frac{3k - 3 - 3k - 3}{2} = \frac{- 6}{2} = - 3.\]

\[k = - 1 \Longrightarrow D = 0 \Longrightarrow\]

\[x = \frac{3k - 3}{2} = \frac{3 \bullet ( - 1) - 3}{2} =\]

\[= \frac{- 3 - 3}{2} = \frac{- 6}{2} = - 3.\]

\[Ответ:x = 3k\ \ и\ x = - 3\ при\ \]

\[k \neq - 1;\ \ \ \]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 3\ \ при\ k = - 1.\]