6/n-2/3=1/2n

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Solution for 6/n-2/3=1/2n equation: 


D( n )

n = 0

n = 0

n = 0

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

6/n-(2/3) = (1/2)*n // - (1/2)*n

6/n-((1/2)*n)-(2/3) = 0

(-1/2)*n+6/n-2/3 = 0

6*n^-1-1/2*n^1-2/3*n^0 = 0

(6*n^0-1/2*n^2-2/3*n^1)/(n^1) = 0 // * n^2

n^1*(6*n^0-1/2*n^2-2/3*n^1) = 0

n^1

(-1/2)*n^2+(-2/3)*n+6 = 0

(-1/2)*n^2+(-2/3)*n+6 = 0

DELTA = (-2/3)^2-(4*6*(-1/2))

DELTA = 112/9

DELTA > 0

n = ((112/9)^(1/2)-(-2/3))/(2*(-1/2)) or n = (-(-2/3)-(112/9)^(1/2))/(2*(-1/2))

n = -((112/9)^(1/2)+2/3) or n = (112/9)^(1/2)-2/3

n in { -((112/9)^(1/2)+2/3), (112/9)^(1/2)-2/3} 

n in { -((112/9)^(1/2)+2/3), (112/9)^(1/2)-2/3 }

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