The number of diagonals in a certain regular polygon is equal to $2$ times the number of sides. How many sides does this polygon have?
The number of diagonals of a n-gon equals : n (n-3)/2
so:
n (n-3)/2 = 2n Solve for n
n^2 - 3n = 4n
n^2 - 7n = 0
n(n-7) = 0 shows n = 7 sides