Diagonals

What x-gon has 54 diagonals?

Correct answer:

x =  12

Step-by-step explanation:

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=2ab±D=11.5±110.25 n1,2=1.5±10.5 n1=12 n2=9  x>0  x=n1=12

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