Answer
10
Work Step by Step
We are given the following equation:
$$ H=\frac{1}{2}(n^2-n)$$
Plugging in 45 for H:
$$ 45=\frac{1}{2}\left(n^2-n\right) \\ n^2-n-90=0 \\ n\left(n+9\right)-10\left(n+9\right)=0 \\ \left(n+9\right)\left(n-10\right)=0 \\n=10$$
Note, the number of people cannot be negative.
