Polygon

The formula for the number of diagonals in a polygon is \(s(s-3) \div 2\), where s is the numberof sides. 

Setting this equal to 2s, we have: \({s(s-3) \over 2} = 2s\)

Solving, we find s = 0 or 7. 

But, s can't be 0, so \(s = \color{brown}\boxed{7}\)

The equation for the  number of  diagonals in a  regular polygon is

n ( n - 3) / 2      where n is the number of  sides

So we have

n (n -3)  / 2  =  2n

n ( n - 3) = 4n

n^2 - 3n  = 4n

n^2 - 7n =  0

n ( n - 7)  = 0

The second factor gives us what we need

n - 7 = 0

n = 7