5y^2+36y-32/y+8

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Solution for 5y^2+36y-32/y+8 equation: 


D( y )

y = 0

y = 0

y = 0

y in (-oo:0) U (0:+oo)

5*y^2+36*y-(32/y)+8 = 0

5*y^2+36*y-32*y^-1+8 = 0

5*y^2+36*y^1-32*y^-1+8*y^0 = 0

(5*y^3+36*y^2+8*y^1-32*y^0)/(y^1) = 0 // * y^2

y^1*(5*y^3+36*y^2+8*y^1-32*y^0) = 0

y^1

5*y^3+36*y^2+8*y-32 = 0

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

1

y = 1

5*y^3+36*y^2+8*y-32 = 17

1

-1

y = -1

5*y^3+36*y^2+8*y-32 = -9

-1

2

y = 2

5*y^3+36*y^2+8*y-32 = 168

2

-2

y = -2

5*y^3+36*y^2+8*y-32 = 56

-2

4

y = 4

5*y^3+36*y^2+8*y-32 = 896

4

-4

y = -4

5*y^3+36*y^2+8*y-32 = 192

-4

8

y = 8

5*y^3+36*y^2+8*y-32 = 4896

8

-8

y = -8

5*y^3+36*y^2+8*y-32 = -352

-8

16

y = 16

5*y^3+36*y^2+8*y-32 = 29792

16

-16

y = -16

5*y^3+36*y^2+8*y-32 = -11424

-16

32

y = 32

5*y^3+36*y^2+8*y-32 = 200928

32

-32

y = -32

5*y^3+36*y^2+8*y-32 = -127264

-32

{ 1/5, -1/5, -1/5, 1/5, 2/5, -2/5, -2/5, 2/5, 4/5, -4/5, -4/5, 4/5, 8/5, -8/5, -8/5, 8/5, 16/5, -16/5, -16/5, 16/5, 32/5, -32/5, -32/5, 32/5 }

1/5

y

1/5

5*y^3+36*y^2+8*y-32 = -28.92

1/5

-1/5

y

-1/5

5*y^3+36*y^2+8*y-32 = -32.2

-1/5

-1/5

y

-1/5

5*y^3+36*y^2+8*y-32 = -32.2

-1/5

1/5

y

1/5

5*y^3+36*y^2+8*y-32 = -28.92

1/5

2/5

y

2/5

5*y^3+36*y^2+8*y-32 = -22.72

2/5

-2/5

y

-2/5

5*y^3+36*y^2+8*y-32 = -29.76

-2/5

-2/5

y

-2/5

5*y^3+36*y^2+8*y-32 = -29.76

-2/5

2/5

y

2/5

5*y^3+36*y^2+8*y-32 = -22.72

2/5

4/5

y

4/5

5*y^3+36*y^2+8*y-32 = 0

4/5

y-4/5

5*y^2+40*y+40

5*y^3+36*y^2+8*y-32

y-4/5

4*y^2-5*y^3

40*y^2+8*y-32

32*y-40*y^2

40*y-32

32-40*y

0

5*y^2+40*y+40 = 0

DELTA = 40^2-(4*5*40)

DELTA = 800

DELTA > 0

y = (800^(1/2)-40)/(2*5) or y = (-800^(1/2)-40)/(2*5)

y = (20*2^(1/2)-40)/10 or y = (-20*2^(1/2)-40)/10

y in { (-20*2^(1/2)-40)/10, (20*2^(1/2)-40)/10, 4/5} 

y in { (-20*2^(1/2)-40)/10, (20*2^(1/2)-40)/10, 4/5 }

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