0 sides and 0 diagonals.  In other words, the polygon is degenerated into a
single point, which has no sides and no diagonals.  In higher geometry courses
that is allowed.  But in lower level geometry it is not.  If you are in a
lower level of geometry, then the answer is "There are no such polygons,
because there must always be 2 fewer diagonals than sides".

Edwin

n sides and    diagonals.


This quantities are equal (given)


    n = 


Simplify


    2n = n*(n-3)

    n^2 - 3n - 2n = 0

    n^2 - 5n = 0

    n*(n-5) = 0.


The roots are  n= 0  and  n= 5.


Of them, only n= 5 is interesting for us.


It is the problem's answer.


ANSWER.  5-sided polygon (pentagon).