Official solution
\[y = 4 + {1 \over {5 + {1 \over y}}}\]
\[ \Rightarrow y = 4 + {y \over {5y + 1}}\]
\[ \Rightarrow 5{y^2} - 20y - 4 = 0\]
\[ \Rightarrow y = {{20 \pm \sqrt {400 + 80} } \over {10}}\]
\[ \Rightarrow y = {{20 \pm 4\sqrt {30} } \over {10}},y > 0\]
\[ \therefore \] \[y = {{10 + 2\sqrt {30} } \over 5}\]