(5/x-3)+1=(30/x^2-9)

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Solution for (5/x-3)+1=(30/x^2-9) equation: 


D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

5/x-3+1 = 30/(x^2)-9 // - 30/(x^2)-9

5/x-(30/(x^2))-3+1+9 = 0

5/x-30*x^-2-3+1+9 = 0

5*x^-1-30*x^-2+7 = 0

t_1 = x^-1

5*t_1^1-30*t_1^2+7 = 0

5*t_1-30*t_1^2+7 = 0

DELTA = 5^2-(-30*4*7)

DELTA = 865

DELTA > 0

t_1 = (865^(1/2)-5)/(-30*2) or t_1 = (-865^(1/2)-5)/(-30*2)

t_1 = (865^(1/2)-5)/(-60) or t_1 = (865^(1/2)+5)/60

t_1 = (865^(1/2)-5)/(-60)

x^-1-((865^(1/2)-5)/(-60)) = 0

1*x^-1 = (865^(1/2)-5)/(-60) // : 1

x^-1 = (865^(1/2)-5)/(-60)

-1 < 0

1/(x^1) = (865^(1/2)-5)/(-60) // * x^1

1 = ((865^(1/2)-5)/(-60))*x^1 // : (865^(1/2)-5)/(-60)

-60*(865^(1/2)-5)^-1 = x^1

x = -60*(865^(1/2)-5)^-1

t_1 = (865^(1/2)+5)/60

x^-1-((865^(1/2)+5)/60) = 0

1*x^-1 = (865^(1/2)+5)/60 // : 1

x^-1 = (865^(1/2)+5)/60

-1 < 0

1/(x^1) = (865^(1/2)+5)/60 // * x^1

1 = ((865^(1/2)+5)/60)*x^1 // : (865^(1/2)+5)/60

60*(865^(1/2)+5)^-1 = x^1

x = 60*(865^(1/2)+5)^-1

x in { -60*(865^(1/2)-5)^-1, 60*(865^(1/2)+5)^-1 }

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