Yes, that is the standard way.
For those who know derivatives, the derivative of the CML is just 1/3. The derivative of the efficient frontier is:
\( \dfrac{a}{2\sqrt{\sigma-0.09}}\equiv \dfrac{a}{2x}\)
Therefore, the equality of slopes implies that:
\(\dfrac{a}{2x}=\dfrac{1}{3}\Rightarrow x=\dfrac{3}{2}a \)
For those who know derivatives, the derivative of the CML is just 1/3. The derivative of the efficient frontier is:
\( \dfrac{a}{2\sqrt{\sigma-0.09}}\equiv \dfrac{a}{2x}\)
Therefore, the equality of slopes implies that:
\(\dfrac{a}{2x}=\dfrac{1}{3}\Rightarrow x=\dfrac{3}{2}a \)
which is equivalent to set the discriminant to 0.