Solve for a
\left\{\begin{matrix}a=\frac{3\left(-b\sqrt{3\left(36-b^{2}\right)}-b^{2}+54\right)}{27-b^{2}}\text{; }a=\frac{3\left(b\sqrt{3\left(36-b^{2}\right)}-b^{2}+54\right)}{27-b^{2}}\text{, }&|b|\neq 3\sqrt{3}\text{ and }|b|\leq 6\\a=-\frac{6\left(27-b^{2}\right)}{b^{2}-54}\text{, }&|b|=3\sqrt{3}\end{matrix}\right.
Solve for b
b=3\sqrt{\frac{3}{a^{2}-6a+36}}\left(a-6\right)
b=-3\sqrt{\frac{3}{a^{2}-6a+36}}\left(a-6\right)
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