math

The number of diagonals, d, in a polygon of n sides is given by the formula d=n^2-3n/2. If a polygon has 90 diagonals, how many sides has it?

a. 8
b. 10
c. 12
d. 15
e. 20

please answer and explain

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  1. just plug in d=90 and solve

    (n^2-3n)/2 - 90 = 0

    quadratics are easy, right?

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  2. I don't think it is easy, can you explain how to do this problem?

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  3. You have a formula for finding d, given n. You are given d, so you need to find n.
    (n^2-3n)/2 = 90
    n^2-3n = 180
    n^2 - 3n - 180 = 0
    (n-15)(n+12) = 0
    n = 15 or -12

    -12 is not a reasonable answer, so n=15 is the solution.

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