Diagonals to find the number of sides, please explain

Find the number of sides in a regular polygon in which the number of diagonals is equal to four times the number of sides.

 

Formula for he number of diagonals in a polygon:  n(n-3)/2

Since the number of diagonals is four times the numbe of sides:  n(n - 3)/2  =  4n

-- cross-multiplying:  n(n - 3)  =  8n

                                  n² - 3n  =  8n

                                 n² - 11n  =  0

                                 n(n - 11)  =  0

So, either  n = 0 (impossible) or  n = 11.