\[(a - 3)\sqrt{x} = a - 3\]
\[\sqrt{x} = \frac{a - 3}{a - 3} = 1\ \ \]
\[x = 1.\]
\[a = 3 \Longrightarrow x - любое.\]
\[a \neq 3 \Longrightarrow x = 1.\]