+118725 Well the answer is n=8
I got this from the graph
https://www.desmos.com/calculator/ncyzikps9l
I also got it from our web2.0calc 
$${\frac{{{\mathtt{n}}}^{{\mathtt{3}}}}{{\mathtt{6}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{{\mathtt{n}}}^{{\mathtt{2}}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{n}}}{{\mathtt{3}}}}{\mathtt{\,-\,}}{\mathtt{120}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{n}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{239}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,\small\textbf+\,}}{\mathtt{11}}\right)}{{\mathtt{2}}}}\\
{\mathtt{n}} = {\frac{\left({\sqrt{{\mathtt{239}}}}{\mathtt{\,\times\,}}{i}{\mathtt{\,-\,}}{\mathtt{11}}\right)}{{\mathtt{2}}}}\\
{\mathtt{n}} = {\mathtt{8}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{n}} = {\mathtt{\,-\,}}\left({\frac{{\mathtt{11}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{7.729\: \!812\: \!416\: \!869\: \!953}}{i}\right)\\
{\mathtt{n}} = {\mathtt{\,-\,}}{\frac{{\mathtt{11}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{7.729\: \!812\: \!416\: \!869\: \!953}}{i}\\
{\mathtt{n}} = {\mathtt{8}}\\
\end{array} \right\}$$
+118725 @@ End of Day Wrap Thurs 21/5/15 Sydney, Australia Time 10:30pm ♪ ♫
Hi all,
Our diligent answerers today were CPhill, Dgb4thebest, Nauseated, Rosala, civonamzuk, thejamesmachine, DarkBlaze347, Radix, MathsGod1, Zacismyname and Heureka. Thanks all
If you would like to comment on other site issues please do so on the Lantern Thread. Thank you.
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FTJ means 'For the juniors'
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♫♪ ♪ ♫ ♬ ♬ MELODY ♬ ♬ ♫♪ ♪ ♫
+118725 Fri 22/5/15
If you would like to comment on other site issues please do so on the Lantern Thread. Thank you.
Interest Posts:
FTJ means 'For the juniors'
1) We are up and going again :)
2) Our points are all over the place again.
3) Rosala has been a member one year to the day! Thank you for your moving tribute Rosala
4) It appears the forums official games is underway - Rosala seems to have it all under control 
5) team deciding
6) Rationalising the denominator and the importance of brackets Thanks Rosala, Zacismyname and Melody.
7) Physics (weight on inclined plane) not answered yet.
8) Another of Civonamzuk's circle specials 
Impressive answer CPhill
9) And another from Civonamzuk Impressive again Chris
10) Which digit will appear the least? (brainteaser from Thejamesmachine) FTJ+ Thanks CPhill and Anon
11) Angle of Depression Thanks Zacixmyname
12) How many sides does the regular polygon have? Thanks CPhill and Melody
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