Chapter 5 - Section 5.7 - Polynomial Equations and Their Applications - Exercise Set - Page 392: 70

$9$ players

We have to determine the number of players $x$ given $36$ games were played. We use the graph of the function $f(x)=\dfrac{x^2-x}{2}$ and draw the horizontal line $y=36$. This line intersects the graph at the point $(9,36)$: therefore there will be $9$ players in the tournament.