Question

In a room of n people, if everyone shakes hands with everyone else, the total number of handshakes is given by n(n-1)/2. If 253 handshakes are made, how many people are there in the room?

please help!

Answer 1

n(n-1)/2 = 253
n^2 - n - 506 = 0
(n+22)(n-23) = 0
n = 23