((32x^3)-(28x^2)-47x-12)/(8x+3)

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Solution for ((32x^3)-(28x^2)-47x-12)/(8x+3) equation: 


D( x )

8*x+3 = 0

8*x+3 = 0

8*x+3 = 0

8*x+3 = 0 // - 3

8*x = -3 // : 8

x = -3/8

x in (-oo:-3/8) U (-3/8:+oo)

(32*x^3-(28*x^2)-(47*x)-12)/(8*x+3) = 0

(32*x^3-28*x^2-47*x-12)/(8*x+3) = 0

32*x^3-28*x^2-47*x-12 = 0

32*x^3-28*x^2-47*x-12 = 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12 }

1

x = 1

32*x^3-28*x^2-47*x-12 = -55

1

-1

x = -1

32*x^3-28*x^2-47*x-12 = -25

-1

2

x = 2

32*x^3-28*x^2-47*x-12 = 38

2

-2

x = -2

32*x^3-28*x^2-47*x-12 = -286

-2

3

x = 3

32*x^3-28*x^2-47*x-12 = 459

3

-3

x = -3

32*x^3-28*x^2-47*x-12 = -987

-3

4

x = 4

32*x^3-28*x^2-47*x-12 = 1400

4

-4

x = -4

32*x^3-28*x^2-47*x-12 = -2320

-4

6

x = 6

32*x^3-28*x^2-47*x-12 = 5610

6

-6

x = -6

32*x^3-28*x^2-47*x-12 = -7650

-6

12

x = 12

32*x^3-28*x^2-47*x-12 = 50688

12

-12

x = -12

32*x^3-28*x^2-47*x-12 = -58776

-12

{ 1/2, -1/2, 1/4, -1/4, 1/8, -1/8, 1/16, -1/16, 1/32, -1/32, -1/2, 1/2, -1/4, 1/4, -1/8, 1/8, -1/16, 1/16, -1/32, 1/32, 2/2, -2/2, 2/4, -2/4, 2/8, -2/8, 2/16, -2/16, 2/32, -2/32, -2/2, 2/2, -2/4, 2/4, -2/8, 2/8, -2/16, 2/16, -2/32, 2/32, 3/2, -3/2, 3/4, -3/4, 3/8, -3/8, 3/16, -3/16, 3/32, -3/32, -3/2, 3/2, -3/4, 3/4, -3/8, 3/8, -3/16, 3/16, -3/32, 3/32, 4/2, -4/2, 4/4, -4/4, 4/8, -4/8, 4/16, -4/16, 4/32, -4/32, -4/2, 4/2, -4/4, 4/4, -4/8, 4/8, -4/16, 4/16, -4/32, 4/32, 6/2, -6/2, 6/4, -6/4, 6/8, -6/8, 6/16, -6/16, 6/32, -6/32, -6/2, 6/2, -6/4, 6/4, -6/8, 6/8, -6/16, 6/16, -6/32, 6/32, 12/2, -12/2, 12/4, -12/4, 12/8, -12/8, 12/16, -12/16, 12/32, -12/32, -12/2, 12/2, -12/4, 12/4, -12/8, 12/8, -12/16, 12/16, -12/32, 12/32 }

1/2

x

1/2

32*x^3-28*x^2-47*x-12 = -38.5

1/2

-1/2

x

-1/2

32*x^3-28*x^2-47*x-12 = 0.5

-1/2

1/4

x

1/4

32*x^3-28*x^2-47*x-12 = -25

1/4

-1/4

x

-1/4

32*x^3-28*x^2-47*x-12 = -2.5

-1/4

1/8

x

1/8

32*x^3-28*x^2-47*x-12 = -18.25

1/8

-1/8

x

-1/8

32*x^3-28*x^2-47*x-12 = -6.625

-1/8

1/16

x

1/16

32*x^3-28*x^2-47*x-12 = -15.0390625

1/16

-1/16

x

-1/16

32*x^3-28*x^2-47*x-12 = -9.1796875

-1/16

1/32

x

1/32

32*x^3-28*x^2-47*x-12 = -13.49511719

1/32

-1/32

x

-1/32

32*x^3-28*x^2-47*x-12 = -10.55957031

-1/32

-1/2

x

-1/2

32*x^3-28*x^2-47*x-12 = 0.5

-1/2

1/2

x

1/2

32*x^3-28*x^2-47*x-12 = -38.5

1/2

-1/4

x

-1/4

32*x^3-28*x^2-47*x-12 = -2.5

-1/4

1/4

x

1/4

32*x^3-28*x^2-47*x-12 = -25

1/4

-1/8

x

-1/8

32*x^3-28*x^2-47*x-12 = -6.625

-1/8

1/8

x

1/8

32*x^3-28*x^2-47*x-12 = -18.25

1/8

-1/16

x

-1/16

32*x^3-28*x^2-47*x-12 = -9.1796875

-1/16

1/16

x

1/16

32*x^3-28*x^2-47*x-12 = -15.0390625

1/16

-1/32

x

-1/32

32*x^3-28*x^2-47*x-12 = -10.55957031

-1/32

1/32

x

1/32

32*x^3-28*x^2-47*x-12 = -13.49511719

1/32

2/2

x

2/2

32*x^3-28*x^2-47*x-12 = -55

2/2

-2/2

x

-2/2

32*x^3-28*x^2-47*x-12 = -25

-2/2

2/4

x

2/4

32*x^3-28*x^2-47*x-12 = -38.5

2/4

-2/4

x

-2/4

32*x^3-28*x^2-47*x-12 = 0.5

-2/4

2/8

x

2/8

32*x^3-28*x^2-47*x-12 = -25

2/8

-2/8

x

-2/8

32*x^3-28*x^2-47*x-12 = -2.5

-2/8

2/16

x

2/16

32*x^3-28*x^2-47*x-12 = -18.25

2/16

-2/16

x

-2/16

32*x^3-28*x^2-47*x-12 = -6.625

-2/16

2/32

x

2/32

32*x^3-28*x^2-47*x-12 = -15.0390625

2/32

-2/32

x

-2/32

32*x^3-28*x^2-47*x-12 = -9.1796875

-2/32

-2/2

x

-2/2

32*x^3-28*x^2-47*x-12 = -25

-2/2

2/2

x

2/2

32*x^3-28*x^2-47*x-12 = -55

2/2

-2/4

x

-2/4

32*x^3-28*x^2-47*x-12 = 0.5

-2/4

2/4

x

2/4

32*x^3-28*x^2-47*x-12 = -38.5

2/4

-2/8

x

-2/8

32*x^3-28*x^2-47*x-12 = -2.5

-2/8

2/8

x

2/8

32*x^3-28*x^2-47*x-12 = -25

2/8

-2/16

x

-2/16

32*x^3-28*x^2-47*x-12 = -6.625

-2/16

2/16

x

2/16

32*x^3-28*x^2-47*x-12 = -18.25

2/16

-2/32

x

-2/32

32*x^3-28*x^2-47*x-12 = -9.1796875

-2/32

2/32

x

2/32

32*x^3-28*x^2-47*x-12 = -15.0390625

2/32

3/2

x

3/2

32*x^3-28*x^2-47*x-12 = -37.5

3/2

-3/2

x

-3/2

32*x^3-28*x^2-47*x-12 = -112.5

-3/2

3/4

x

3/4

32*x^3-28*x^2-47*x-12 = -49.5

3/4

-3/4

x

-3/4

32*x^3-28*x^2-47*x-12 = -6

-3/4

3/8

x

3/8

32*x^3-28*x^2-47*x-12 = -31.875

3/8

-3/8

x

-3/8

32*x^3-28*x^2-47*x-12 = 0

-3/8

x+3/8

32*x^2-40*x-32

32*x^3-28*x^2-47*x-12

x+3/8

-32*x^3-12*x^2

-40*x^2-47*x-12

40*x^2+15*x

-32*x-12

32*x+12

0

32*x^2-40*x-32 = 0

DELTA = (-40)^2-(-32*4*32)

DELTA = 5696

DELTA > 0

x = (5696^(1/2)+40)/(2*32) or x = (40-5696^(1/2))/(2*32)

x = (8*89^(1/2)+40)/64 or x = (40-8*89^(1/2))/64

x in { (40-8*89^(1/2))/64, (8*89^(1/2)+40)/64, -3/8} 

(x-((40-8*89^(1/2))/64))*(x-((8*89^(1/2)+40)/64))*(x+3/8) = 0

((x-((40-8*89^(1/2))/64))*(x-((8*89^(1/2)+40)/64))*(x+3/8))/(8*x+3) = 0

( x+3/8 )

x+3/8 = 0 // - 3/8

x = -3/8

( x-((40-8*89^(1/2))/64) )

x-((40-8*89^(1/2))/64) = 0 // + (40-8*89^(1/2))/64

x = (40-8*89^(1/2))/64

( x-((8*89^(1/2)+40)/64) )

x-((8*89^(1/2)+40)/64) = 0 // + (8*89^(1/2)+40)/64

x = (8*89^(1/2)+40)/64

x in { -3/8} 

x in { (40-8*89^(1/2))/64, (8*89^(1/2)+40)/64 }

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