2=-8/x-5/x^2

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Solution for 2=-8/x-5/x^2 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 = -8/x-(5/(x^2)) // + -8/x-(5/(x^2))

5/(x^2)-(-8/x)+2 = 0

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

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

t_1 = x^-1

5*t_1^2+8*t_1^1+2 = 0

5*t_1^2+8*t_1+2 = 0

DELTA = 8^2-(2*4*5)

DELTA = 24

DELTA > 0

t_1 = (24^(1/2)-8)/(2*5) or t_1 = (-24^(1/2)-8)/(2*5)

t_1 = (2*6^(1/2)-8)/10 or t_1 = (-2*6^(1/2)-8)/10

t_1 = (-2*6^(1/2)-8)/10

x^-1-((-2*6^(1/2)-8)/10) = 0

1*x^-1 = (-2*6^(1/2)-8)/10 // : 1

x^-1 = (-2*6^(1/2)-8)/10

-1 < 0

1/(x^1) = (-2*6^(1/2)-8)/10 // * x^1

1 = ((-2*6^(1/2)-8)/10)*x^1 // : (-2*6^(1/2)-8)/10

10*(-2*6^(1/2)-8)^-1 = x^1

x = 10*(-2*6^(1/2)-8)^-1

t_1 = (2*6^(1/2)-8)/10

x^-1-((2*6^(1/2)-8)/10) = 0

1*x^-1 = (2*6^(1/2)-8)/10 // : 1

x^-1 = (2*6^(1/2)-8)/10

-1 < 0

1/(x^1) = (2*6^(1/2)-8)/10 // * x^1

1 = ((2*6^(1/2)-8)/10)*x^1 // : (2*6^(1/2)-8)/10

10*(2*6^(1/2)-8)^-1 = x^1

x = 10*(2*6^(1/2)-8)^-1

x in { 10*(-2*6^(1/2)-8)^-1, 10*(2*6^(1/2)-8)^-1 }

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