\[\begin{array}{l}
\sqrt {5{\rm{x}} + 6} = x - 6\\
dk:x \ge \frac{{ - 6}}{5}\\
\Leftrightarrow \left\{ \begin{array}{l}
x - 6 \ge 0\\
5{\rm{x}} + 6 = {\left( {x - 6} \right)^2}
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x \ge 6\\
5{\rm{x}} + 6 = {x^2} - 12{\rm{x}} + 36
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\begin{array}{*{20}{l}}
{x \ge 6}
\end{array}\\
{x^2} - 17{\rm{x}} + 30 = 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\begin{array}{*{20}{l}}
{x \ge 6}
\end{array}\\
{x^2} - 2{\rm{x}} - 15{\rm{x}} + 30 = 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\begin{array}{*{20}{l}}
{x \ge 6}
\end{array}\\
x\left( {x - 2} \right) - 15\left( {x - 2} \right) = 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\begin{array}{*{20}{l}}
{x \ge 6}
\end{array}\\
\left( {x - 2} \right)\left( {x - 15} \right) = 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\begin{array}{*{20}{l}}
{x \ge 6}
\end{array}\\
\left[ \begin{array}{l}
x - 2 = 0\\
x - 15 = 0
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\begin{array}{*{20}{l}}
{x \ge 6}
\end{array}\\
\left[ \begin{array}{l}
x = 2\\
x = 15
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow x = 15\left( {tm} \right)\\
vay:x = 15
\end{array}\]