Chapter 5 - Polynomials and Factoring - 5.8 Solving Applications - 5.8 Exercise Set - Page 360: 26

15

We are given the following equation: $$ H=\frac{1}{2}(n^2-n)$$ Plugging in $105$ for $H$, we find: $$105=\frac{1}{2}\left(n^2-n\right) \\ n^2-n-210=0 \\ n_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\cdot \:1\left(-210\right)}}{2\cdot \:1}$$ Considering only positive values: $$ n=15$$