Answer
7 sides
Work Step by Step
$D = 1/2 * n * (n-3)$
14 diagonals
$D = 1/2 * n * (n-3)$
$14 = 1/2 *n^2-3n$
$14*2 =2* 1/2 *n^2-3n$
$28 = n^2-3n$
$n^2-3n-28=0$
$n^2-7n+4n-28=0$
$n(n-7)+4(n-7)=0$
$(n+4)(n-7)=0$
$n+4=0$
$n=-4$ (not a valid answer since we can't have a negative number of sides)
$n-7=0$
$n=7$
