-2/x^2-9=x-4/x^2-3x

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Solution for -2/x^2-9=x-4/x^2-3x equation: 


D( x )

x^2 = 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^2)-9 = x-(3*x)-(4/(x^2)) // - x-(3*x)-(4/(x^2))

3*x-x-2/(x^2)+4/(x^2)-9 = 0

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

(2*x^3-9*x^2+2*x^0)/(x^2) = 0 // * x^4

x^2*(2*x^3-9*x^2+2*x^0) = 0

x^2

2*x^3-9*x^2+2 = 0

{ 1, -1, 2, -2 }

1

x = 1

2*x^3-9*x^2+2 = -5

1

-1

x = -1

2*x^3-9*x^2+2 = -9

-1

2

x = 2

2*x^3-9*x^2+2 = -18

2

-2

x = -2

2*x^3-9*x^2+2 = -50

-2

{ 1/2, -1/2, -1/2, 1/2, 2/2, -2/2, -2/2, 2/2 }

1/2

x

1/2

2*x^3-9*x^2+2 = 0

1/2

x-1/2

2*x^2-8*x-4

2*x^3-9*x^2+2

x-1/2

x^2-2*x^3

2-8*x^2

8*x^2-4*x

2-4*x

4*x-2

0

2*x^2-8*x-4 = 0

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

DELTA = 96

DELTA > 0

x = (96^(1/2)+8)/(2*2) or x = (8-96^(1/2))/(2*2)

x = (4*6^(1/2)+8)/4 or x = (8-4*6^(1/2))/4

x in { (8-4*6^(1/2))/4, (4*6^(1/2)+8)/4, 1/2} 

x in { (8-4*6^(1/2))/4, (4*6^(1/2)+8)/4, 1/2 }

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