Polygon 42

Which polygon has 42 more diagonals than sides?

Correct result:

n =  12

Solution:

12n(n3)=n+42 n25n84=0  a=1;b=5;c=84 D=b24ac=5241(84)=361 D>0  n1,2=b±D2a=5±3612 n1,2=5±192 n1,2=2.5±9.5 n1=12 n2=7   Factored form of the equation:  (n12)(n+7)=0   n>0 n=12

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