190(n-2)=160/n

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Solution for 190(n-2)=160/n equation:


D( n )

n = 0

n = 0

n = 0

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

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

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

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

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

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

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

190*n^2-380*n-160 = 0

190*n^2-380*n-160 = 0

10*(19*n^2-38*n-16) = 0

19*n^2-38*n-16 = 0

DELTA = (-38)^2-(-16*4*19)

DELTA = 2660

DELTA > 0

n = (2660^(1/2)+38)/(2*19) or n = (38-2660^(1/2))/(2*19)

n = (2*665^(1/2)+38)/38 or n = (38-2*665^(1/2))/38

10*(n-((38-2*665^(1/2))/38))*(n-((2*665^(1/2)+38)/38)) = 0

(10*(n-((38-2*665^(1/2))/38))*(n-((2*665^(1/2)+38)/38)))/n = 0

(10*(n-((38-2*665^(1/2))/38))*(n-((2*665^(1/2)+38)/38)))/n = 0 // * n

10*(n-((38-2*665^(1/2))/38))*(n-((2*665^(1/2)+38)/38)) = 0

( 10 )

10 = 0

n belongs to the empty set

( n-((2*665^(1/2)+38)/38) )

n-((2*665^(1/2)+38)/38) = 0 // + (2*665^(1/2)+38)/38

n = (2*665^(1/2)+38)/38

( n-((38-2*665^(1/2))/38) )

n-((38-2*665^(1/2))/38) = 0 // + (38-2*665^(1/2))/38

n = (38-2*665^(1/2))/38

n in { (2*665^(1/2)+38)/38, (38-2*665^(1/2))/38 }

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