College Algebra (6th Edition)

$9$ players
Plug the given number of games into the formula. Then multiply by the denominator on both sides and put all terms on one side. Then solve by finding two $x$-values that equal the third term when multiplied and add up to the coefficient of the second term. $N=\frac{x^2-x}{2}$ $36=\frac{x^2-x}{2}$ $72=x^2-x$ $x^2-x-72=0$ $(x+8)(x-9)=0$ $x=-8,9$ $x=9$ Only the positive value will matter since the question is asking for the number of players who were entered in the tournament.