Question

A polygon has 35 diagonals. How many sides does it have?

Answer 1

$d=35\\ d=\frac{n(n-3)}{2}\\ d=\frac{n(n-3)}{2}\\35=\frac{n(n-3)}{2}\\ 70=n^2-3n\\ n^2-3n-70=0\\ n^2-10n+7n-70=0\\ n(n-10)+7(n-10)=0\\ (n+7)(n-10)=0\\ n=-7 \vee n=10\\\\ n=10$