+118723 $$\begin{array}{rll}
\frac{5n}{2}&=&\frac{8}{(3n-24)}\\\\
2(3n-24)\times\frac{5n}{2}&=&\frac{8}{(3n-24)}\times2 (3n-24)\\\\
(3n-24)\times5n&=&8\times2\\\\
15n^2-120n&=&16\\\\
15n^2-120n-16&=&0\\\\
\end{array}$$
$${\sqrt{{{\mathtt{120}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{15}}{\mathtt{\,\times\,}}{\mathtt{16}}}} = {\sqrt{\left({\mathtt{16}}{\mathtt{\,\times\,}}{\mathtt{4}}{\mathtt{\,\times\,}}\left({{\mathtt{15}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{15}}\right)\right)}} = {\mathtt{8}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{240}}}} = {\mathtt{16}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{60}}}} = {\mathtt{32}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{15}}}}$$
$$\\n=\frac{120\pm32\sqrt{15}}{30}\\\\
n=\frac{60\pm16\sqrt{15}}{15}\\\\$$
+118723 $$\begin{array}{rll}
\frac{5n}{2}&=&\frac{8}{(3n-24)}\\\\
2(3n-24)\times\frac{5n}{2}&=&\frac{8}{(3n-24)}\times2 (3n-24)\\\\
(3n-24)\times5n&=&8\times2\\\\
15n^2-120n&=&16\\\\
15n^2-120n-16&=&0\\\\
\end{array}$$
$${\sqrt{{{\mathtt{120}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{15}}{\mathtt{\,\times\,}}{\mathtt{16}}}} = {\sqrt{\left({\mathtt{16}}{\mathtt{\,\times\,}}{\mathtt{4}}{\mathtt{\,\times\,}}\left({{\mathtt{15}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{15}}\right)\right)}} = {\mathtt{8}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{240}}}} = {\mathtt{16}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{60}}}} = {\mathtt{32}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{15}}}}$$
$$\\n=\frac{120\pm32\sqrt{15}}{30}\\\\
n=\frac{60\pm16\sqrt{15}}{15}\\\\$$
