(-18x^3+17x+6)/(3x+2)

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Solution for (-18x^3+17x+6)/(3x+2) equation: 


D( x )

3*x+2 = 0

3*x+2 = 0

3*x+2 = 0

3*x+2 = 0 // - 2

3*x = -2 // : 3

x = -2/3

x in (-oo:-2/3) U (-2/3:+oo)

(17*x-18*x^3+6)/(3*x+2) = 0

17*x-18*x^3+6 = 0

17*x-18*x^3+6 = 0

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

1

x = 1

17*x-18*x^3+6 = 5

1

-1

x = -1

17*x-18*x^3+6 = 7

-1

2

x = 2

17*x-18*x^3+6 = -104

2

-2

x = -2

17*x-18*x^3+6 = 116

-2

3

x = 3

17*x-18*x^3+6 = -429

3

-3

x = -3

17*x-18*x^3+6 = 441

-3

6

x = 6

17*x-18*x^3+6 = -3780

6

-6

x = -6

17*x-18*x^3+6 = 3792

-6

{ 1/2, -1/2, 1/3, -1/3, 1/6, -1/6, 1/9, -1/9, 1/18, -1/18, -1/2, 1/2, -1/3, 1/3, -1/6, 1/6, -1/9, 1/9, -1/18, 1/18, 2/2, -2/2, 2/3, -2/3, 2/6, -2/6, 2/9, -2/9, 2/18, -2/18, -2/2, 2/2, -2/3, 2/3, -2/6, 2/6, -2/9, 2/9, -2/18, 2/18, 3/2, -3/2, 3/3, -3/3, 3/6, -3/6, 3/9, -3/9, 3/18, -3/18, -3/2, 3/2, -3/3, 3/3, -3/6, 3/6, -3/9, 3/9, -3/18, 3/18, 6/2, -6/2, 6/3, -6/3, 6/6, -6/6, 6/9, -6/9, 6/18, -6/18, -6/2, 6/2, -6/3, 6/3, -6/6, 6/6, -6/9, 6/9, -6/18, 6/18 }

1/2

x

1/2

17*x-18*x^3+6 = 12.25

1/2

-1/2

x

-1/2

17*x-18*x^3+6 = -0.25

-1/2

1/3

x

1/3

17*x-18*x^3+6 = 11

1/3

-1/3

x

-1/3

17*x-18*x^3+6 = 1

-1/3

1/6

x

1/6

17*x-18*x^3+6 = 8.75

1/6

-1/6

x

-1/6

17*x-18*x^3+6 = 3.25

-1/6

1/9

x

1/9

17*x-18*x^3+6 = 7.86419753

1/9

-1/9

x

-1/9

17*x-18*x^3+6 = 4.13580247

-1/9

1/18

x

1/18

17*x-18*x^3+6 = 6.94135802

1/18

-1/18

x

-1/18

17*x-18*x^3+6 = 5.05864198

-1/18

-1/2

x

-1/2

17*x-18*x^3+6 = -0.25

-1/2

1/2

x

1/2

17*x-18*x^3+6 = 12.25

1/2

-1/3

x

-1/3

17*x-18*x^3+6 = 1

-1/3

1/3

x

1/3

17*x-18*x^3+6 = 11

1/3

-1/6

x

-1/6

17*x-18*x^3+6 = 3.25

-1/6

1/6

x

1/6

17*x-18*x^3+6 = 8.75

1/6

-1/9

x

-1/9

17*x-18*x^3+6 = 4.13580247

-1/9

1/9

x

1/9

17*x-18*x^3+6 = 7.86419753

1/9

-1/18

x

-1/18

17*x-18*x^3+6 = 5.05864198

-1/18

1/18

x

1/18

17*x-18*x^3+6 = 6.94135802

1/18

2/2

x

2/2

17*x-18*x^3+6 = 5

2/2

-2/2

x

-2/2

17*x-18*x^3+6 = 7

-2/2

2/3

x

2/3

17*x-18*x^3+6 = 12

2/3

-2/3

x

-2/3

17*x-18*x^3+6 = 0

-2/3

x+2/3

12*x-18*x^2+9

17*x-18*x^3+6

x+2/3

18*x^3+12*x^2

12*x^2+17*x+6

-12*x^2-8*x

9*x+6

-9*x-6

0

12*x-18*x^2+9 = 0

DELTA = 12^2-(-18*4*9)

DELTA = 792

DELTA > 0

x = (792^(1/2)-12)/(-18*2) or x = (-792^(1/2)-12)/(-18*2)

x = (6*22^(1/2)-12)/(-36) or x = (-6*22^(1/2)-12)/(-36)

x in { (6*22^(1/2)-12)/(-36), (-6*22^(1/2)-12)/(-36), -2/3} 

(x-((6*22^(1/2)-12)/(-36)))*(x-((-6*22^(1/2)-12)/(-36)))*(x+2/3) = 0

((x-((6*22^(1/2)-12)/(-36)))*(x-((-6*22^(1/2)-12)/(-36)))*(x+2/3))/(3*x+2) = 0

( x+2/3 )

x+2/3 = 0 // - 2/3

x = -2/3

( x-((-6*22^(1/2)-12)/(-36)) )

x-((-6*22^(1/2)-12)/(-36)) = 0 // + (-6*22^(1/2)-12)/(-36)

x = (-6*22^(1/2)-12)/(-36)

( x-((6*22^(1/2)-12)/(-36)) )

x-((6*22^(1/2)-12)/(-36)) = 0 // + (6*22^(1/2)-12)/(-36)

x = (6*22^(1/2)-12)/(-36)

x in { -2/3} 

x in { (-6*22^(1/2)-12)/(-36), (6*22^(1/2)-12)/(-36) }

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