2/x=1/x^2-5

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Solution for 2/x=1/x^2-5 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)

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

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

2/x-x^-2+5 = 0

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

t_1 = x^-1

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

2*t_1-t_1^2+5 = 0

DELTA = 2^2-(-1*4*5)

DELTA = 24

DELTA > 0

t_1 = (24^(1/2)-2)/(-1*2) or t_1 = (-24^(1/2)-2)/(-1*2)

t_1 = (2*6^(1/2)-2)/(-2) or t_1 = (-2*6^(1/2)-2)/(-2)

t_1 = (2*6^(1/2)-2)/(-2)

x^-1-((2*6^(1/2)-2)/(-2)) = 0

1*x^-1 = (2*6^(1/2)-2)/(-2) // : 1

x^-1 = (2*6^(1/2)-2)/(-2)

-1 < 0

1/(x^1) = (2*6^(1/2)-2)/(-2) // * x^1

1 = ((2*6^(1/2)-2)/(-2))*x^1 // : (2*6^(1/2)-2)/(-2)

-2*(2*6^(1/2)-2)^-1 = x^1

x = -2*(2*6^(1/2)-2)^-1

t_1 = (-2*6^(1/2)-2)/(-2)

x^-1-((-2*6^(1/2)-2)/(-2)) = 0

1*x^-1 = (-2*6^(1/2)-2)/(-2) // : 1

x^-1 = (-2*6^(1/2)-2)/(-2)

-1 < 0

1/(x^1) = (-2*6^(1/2)-2)/(-2) // * x^1

1 = ((-2*6^(1/2)-2)/(-2))*x^1 // : (-2*6^(1/2)-2)/(-2)

-2*(-2*6^(1/2)-2)^-1 = x^1

x = -2*(-2*6^(1/2)-2)^-1

x in { -2*(2*6^(1/2)-2)^-1, -2*(-2*6^(1/2)-2)^-1 }

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