From the condition, we have these two equations


m + n = 9,                (counting the sides)

 +  = 7    (counting the diagonals).



Equivalently

m + n = 9,                

 +  = 14.



Equivalently

m + n = 9,                

 +  = 14.
    


Equivalently

m + n = 9,                

 +  = 14 + 3*(m+n) = 14 + 3*9 = 14 +27 = 41.



Thus you have these two equations

m + n = 9,         (1)

m^2 + n^2 = 41.    (2)



From (1), express m = 9-n  and substitute it into (2).
You will get a quadratic equation. Solve it by any way you want.



Answer.  4 sides and 5 sides.