\(\dfrac{8}{3}n^2+36n=2400< =>\dfrac{8}{3}n^2+36n-2400=0\)
\(< =>\dfrac{8}{3}\left(n^2+\dfrac{27}{2}n-900\right)=0\)
\(=>n^2+\dfrac{27}{2}n-900=0\)
\(< =>n^2+2.\dfrac{27}{4}n+\left(\dfrac{27}{4}\right)^2-\left(\dfrac{27}{4}\right)^2-900=0\)
\(< =>\left(n+\dfrac{27}{4}\right)^2-\left(\dfrac{15129}{16}\right)=0\)
\(< =>\left(n+\dfrac{27}{4}\right)^2-\left(\dfrac{123}{4}\right)^2=0\)
\(< =>\left(n+\dfrac{75}{2}\right)\left(n-24\right)=0\)
\(=>\left[{}\begin{matrix}n+\dfrac{75}{2}=0\\n-24=0\end{matrix}\right.< =>\left[{}\begin{matrix}n=-\dfrac{75}{2}=-37,5\\n=24\end{matrix}\right.\)
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