How do you find the number of sides a polygon has when it has 104 diagonals?

Let the number of sides be x and use the diagonal formula:

1/2*(x2-3x) = 104

Multiply both sides by 2:

x2-3x = 208

Subtract 208 from both sides:

x2-3x-208 = 0

Solving the above by means of the quadratic equation formula gives x a value of -13 and 16 so it must have 16 sides

Check: 1/2*(162-(3*16)) = 104 diagonals