Given,

\[{{x}^{2}}~+\text{ }6{{y}^{2}}~=\text{ }5xy\]

Dividing by y² both side, we have

Let

\[\begin{array}{*{35}{l}}

x/y\text{ }=\text{ }a  \\

=>\text{ }{{a}^{2}}~\text{ }-5a\text{ }+\text{ }6\text{ }=\text{ }0  \\

\left( a\text{ }\text{ }-2 \right)\text{ }\left( a\text{ }\text{ }-3 \right)\text{ }=\text{ }0  \\

a\text{ }=\text{ }2\text{ }or\text{ }a\text{ }=\text{ }3  \\

\end{array}\]

Therefore, x/y = 2 or 3