Diagonals

What x-gon has 54 diagonals?

Correct result:

x =  12

Solution:

54=n(n3)/2  0.5n2+1.5n+54=0 0.5n21.5n54=0  a=0.5;b=1.5;c=54 D=b24ac=1.5240.5(54)=110.25 D>0  n1,2=b±D2a=1.5±110.251 n1,2=1.5±10.5 n1=12 n2=9   Factored form of the equation:  0.5(n12)(n+9)=0  x>0  x=n1=12

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