8*x-(1000/(x^2))=0

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Solution for 8*x-(1000/(x^2))=0 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)

8*x-(1000/(x^2)) = 0

8*x-1000*x^-2 = 0

8*x^1-1000*x^-2 = 0

(8*x^3-1000*x^0)/(x^2) = 0 // * x^4

x^2*(8*x^3-1000*x^0) = 0

x^2

8*x^3-1000 = 0

{ 1, -1, 2, -2, 4, -4, 5, -5, 8, -8, 10, -10, 20, -20, 25, -25, 40, -40, 50, -50, 100, -100, 125, -125, 200, -200, 250, -250, 500, -500, 1000, -1000 }

1

x = 1

8*x^3-1000 = -992

1

-1

x = -1

8*x^3-1000 = -1008

-1

2

x = 2

8*x^3-1000 = -936

2

-2

x = -2

8*x^3-1000 = -1064

-2

4

x = 4

8*x^3-1000 = -488

4

-4

x = -4

8*x^3-1000 = -1512

-4

5

x = 5

8*x^3-1000 = 0

5

x-5

8*x^2+40*x+200

8*x^3-1000

x-5

40*x^2-8*x^3

40*x^2-1000

200*x-40*x^2

200*x-1000

1000-200*x

0

8*x^2+40*x+200 = 0

DELTA = 40^2-(4*8*200)

DELTA = -4800

DELTA < 0

x in { 5} 

x = 5

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