How many people were at a party if There were 105 handshakes at a party and if each person at the party shook hands with exactly once with every other person. The answer is 15. How do I write the problem?

Question

How many people were at a party if There were 105 handshakes at a party and if each person at the party shook hands with exactly once with every other person.  The answer is 15.  How do I write the problem?

makhan pal · Accepted Answer

n(n-1)/2=105, > n^2-n-210=0, n^2-15n+14n-210=0, > n(n-15)+14(n-15)=0, >(n-15)(n+14)=0, so, n=15, =-14 , as -ve is not possible, so n=15, ans will be 15 men

Brawl stars · Answer

15