180(n-2)=160/n

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Solution for 180(n-2)=160/n equation:


D( n )

n = 0

n = 0

n = 0

n in (-oo:0) U (0:+oo)

180*(n-2) = 160/n // - 160/n

180*(n-2)-(160/n) = 0

180*(n-2)-160*n^-1 = 0

180*(n-2)-160/n = 0

(180*n*(n-2))/n-160/n = 0

180*n*(n-2)-160 = 0

180*n^2-360*n-160 = 0

180*n^2-360*n-160 = 0

20*(9*n^2-18*n-8) = 0

9*n^2-18*n-8 = 0

DELTA = (-18)^2-(-8*4*9)

DELTA = 612

DELTA > 0

n = (612^(1/2)+18)/(2*9) or n = (18-612^(1/2))/(2*9)

n = (6*17^(1/2)+18)/18 or n = (18-6*17^(1/2))/18

20*(n-((18-6*17^(1/2))/18))*(n-((6*17^(1/2)+18)/18)) = 0

(20*(n-((18-6*17^(1/2))/18))*(n-((6*17^(1/2)+18)/18)))/n = 0

(20*(n-((18-6*17^(1/2))/18))*(n-((6*17^(1/2)+18)/18)))/n = 0 // * n

20*(n-((18-6*17^(1/2))/18))*(n-((6*17^(1/2)+18)/18)) = 0

( 20 )

20 = 0

n belongs to the empty set

( n-((18-6*17^(1/2))/18) )

n-((18-6*17^(1/2))/18) = 0 // + (18-6*17^(1/2))/18

n = (18-6*17^(1/2))/18

( n-((6*17^(1/2)+18)/18) )

n-((6*17^(1/2)+18)/18) = 0 // + (6*17^(1/2)+18)/18

n = (6*17^(1/2)+18)/18

n in { (18-6*17^(1/2))/18, (6*17^(1/2)+18)/18 }

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