(8/x^2)+(9/x)+2=0

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Solution for (8/x^2)+(9/x)+2=0 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)

9/x+8/(x^2)+2 = 0

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

t_1 = x^-1

8*t_1^2+9*t_1^1+2 = 0

8*t_1^2+9*t_1+2 = 0

DELTA = 9^2-(2*4*8)

DELTA = 17

DELTA > 0

t_1 = (17^(1/2)-9)/(2*8) or t_1 = (-17^(1/2)-9)/(2*8)

t_1 = (17^(1/2)-9)/16 or t_1 = (-(17^(1/2)+9))/16

t_1 = (-(17^(1/2)+9))/16

x^-1-((-(17^(1/2)+9))/16) = 0

x^-1+(1/16)*(17^(1/2)+9) = 0

1*x^-1 = -(1/16*(17^(1/2)+9)) // : 1

x^-1 = -1/16*(17^(1/2)+9)

-1 < 0

1/(x^1) = -1/16*(17^(1/2)+9) // * x^1

1 = -1/16*(17^(1/2)+9)*x^1 // : -1/16*(17^(1/2)+9)

-16*(17^(1/2)+9)^-1 = x^1

x = -16*(17^(1/2)+9)^-1

t_1 = (17^(1/2)-9)/16

x^-1-((17^(1/2)-9)/16) = 0

1*x^-1 = (17^(1/2)-9)/16 // : 1

x^-1 = (17^(1/2)-9)/16

-1 < 0

1/(x^1) = (17^(1/2)-9)/16 // * x^1

1 = ((17^(1/2)-9)/16)*x^1 // : (17^(1/2)-9)/16

16*(17^(1/2)-9)^-1 = x^1

x = 16*(17^(1/2)-9)^-1

x in { -16*(17^(1/2)+9)^-1, 16*(17^(1/2)-9)^-1 }

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