I suggest you (a) use symbols -- say, P, Q, and R -- for some of the repeated terms and (b) replace all \left and \right directives with non-autosizing alternatives. And, do use [...]^{1/2} notation for the really large square-root term. Last (and definitely least) I'd replace \sqrt{\frac{3}{2}} with \sqrt{1.5}.
\documentclass{article}\usepackage{amsmath}\newcommand\TR{\tilde{r}}\newcommand\TG{\tilde{g}}\begin{document}\noindentPut $P=\sqrt{\TG^2+\TR^2}$, $Q=\sqrt{\TG^2+\TR_h^2}$, and $R=\TR_h^2+1$. Then\begin{equation}\begin{split} \lambda &= \sqrt{1.5} \Bigl(\frac{1}{\TR (P^2)^{7/4} \TR_h}\Bigr) \Bigl\{- %\Bigl[ \Bigl[-\bigl(\TR^2 R (Q^2/P^2)^{3/2}\bigr)\big/ \TR_h^2+\TR^2+1\Bigr] \\&\quad \times\Bigl[2 \TG^6 P \TR_h^2+\TG^4 (\TR^4 R Q+6 \TR^2 P \TR_h^2)+\TG^2 \TR^4 \bigl(\TR_h^4 Q+\TR_h^2 (-4 \TR^2 Q \\&\qquad +Q+6P) -4 \TR^2 Q\bigr)+2 \TR^6\TR_h^2 (-2 \TR_h^2 Q-2 Q+P) \Bigr] %\Bigr] \Bigr\}^{1/2} \end{split}\end{equation}\end{document}