When "n" number of people then number of people is:
[tex]\text{handshakes}=\frac{n(n-1)}{2}[/tex]If the handshakes is 25 then:
[tex]25=\frac{n(n-1)}{2}[/tex][tex]\begin{gathered} 25\times2=n(n-1) \\ 50=n^2-n \\ n^2-n-50=0 \\ \end{gathered}[/tex]Solve the equation:
[tex]\begin{gathered} n=\frac{-(-1)\pm\sqrt[]{1-4(1)(-50)}}{2} \\ n=\frac{1\pm\sqrt[]{1+200}}{2} \\ n\approx7 \end{gathered}[/tex]So 7 friends still at the party.
