1/n-5=9/n2-25

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Solution for 1/n-5=9/n2-25 equation: 


D( n )

n = 0

n^2 = 0

n = 0

n = 0

n^2 = 0

n^2 = 0

1*n^2 = 0 // : 1

n^2 = 0

n = 0

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

1/n-5 = 9/(n^2)-25 // - 9/(n^2)-25

1/n-(9/(n^2))-5+25 = 0

1/n-9*n^-2-5+25 = 0

n^-1-9*n^-2+20 = 0

t_1 = n^-1

1*t_1^1-9*t_1^2+20 = 0

t_1-9*t_1^2+20 = 0

DELTA = 1^2-(-9*4*20)

DELTA = 721

DELTA > 0

t_1 = (721^(1/2)-1)/(-9*2) or t_1 = (-721^(1/2)-1)/(-9*2)

t_1 = (721^(1/2)-1)/(-18) or t_1 = (721^(1/2)+1)/18

t_1 = (721^(1/2)-1)/(-18)

n^-1-((721^(1/2)-1)/(-18)) = 0

1*n^-1 = (721^(1/2)-1)/(-18) // : 1

n^-1 = (721^(1/2)-1)/(-18)

-1 < 0

1/(n^1) = (721^(1/2)-1)/(-18) // * n^1

1 = ((721^(1/2)-1)/(-18))*n^1 // : (721^(1/2)-1)/(-18)

-18*(721^(1/2)-1)^-1 = n^1

n = -18*(721^(1/2)-1)^-1

t_1 = (721^(1/2)+1)/18

n^-1-((721^(1/2)+1)/18) = 0

1*n^-1 = (721^(1/2)+1)/18 // : 1

n^-1 = (721^(1/2)+1)/18

-1 < 0

1/(n^1) = (721^(1/2)+1)/18 // * n^1

1 = ((721^(1/2)+1)/18)*n^1 // : (721^(1/2)+1)/18

18*(721^(1/2)+1)^-1 = n^1

n = 18*(721^(1/2)+1)^-1

n in { -18*(721^(1/2)-1)^-1, 18*(721^(1/2)+1)^-1 }

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