Feb 29, A Unique Day - 2

$\begin{aligned} N & = \frac{\displaystyle \sum_{x=29}^{200} \frac{x^3-2x^2} {x^2}}{\displaystyle \sum_{x=2}^{29} \frac{x^3-2x^2}{x^2}} = \frac{ \displaystyle \sum^{200}_{x=29}x-2 }{ \displaystyle \sum^{29}_{x=2}x-2 } \\ & = \frac{ \displaystyle \sum^{198}_{n=27}x }{ \displaystyle \sum^{27}_{x=0}x } = \frac{ \displaystyle \sum^{198}_{x=1}x-\displaystyle \sum^{26}_{x=1}x }{ \displaystyle \sum^{27}_{x=0}x } \\ & = \frac{ \frac{198\cdot 199}{2}-\frac{26\cdot 27}{2} }{\frac{27\cdot 28}{2}}=51.19 \\ \Rightarrow \lfloor N \rfloor & = \lfloor 51.19 \rfloor=\boxed{51} \end{aligned}$