2x=(128/(x^2))

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Solution for 2x=(128/(x^2)) 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 = 128/(x^2) // - 128/(x^2)

2*x-(128/(x^2)) = 0

2*x-128*x^-2 = 0

2*x^1-128*x^-2 = 0

(2*x^3-128*x^0)/(x^2) = 0 // * x^4

x^2*(2*x^3-128*x^0) = 0

x^2

2*x^3-128 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8, 16, -16, 32, -32, 64, -64, 128, -128 }

1

x = 1

2*x^3-128 = -126

1

-1

x = -1

2*x^3-128 = -130

-1

2

x = 2

2*x^3-128 = -112

2

-2

x = -2

2*x^3-128 = -144

-2

4

x = 4

2*x^3-128 = 0

4

x-4

2*x^2+8*x+32

2*x^3-128

x-4

8*x^2-2*x^3

8*x^2-128

32*x-8*x^2

32*x-128

128-32*x

0

2*x^2+8*x+32 = 0

DELTA = 8^2-(2*4*32)

DELTA = -192

DELTA < 0

x in { 4} 

x = 4

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