(9x^3+15x^2-24x-16)/(3x-4)

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Solution for (9x^3+15x^2-24x-16)/(3x-4) equation: 


D( x )

3*x-4 = 0

3*x-4 = 0

3*x-4 = 0

3*x-4 = 0 // + 4

3*x = 4 // : 3

x = 4/3

x in (-oo:4/3) U (4/3:+oo)

(9*x^3+15*x^2-(24*x)-16)/(3*x-4) = 0

(9*x^3+15*x^2-24*x-16)/(3*x-4) = 0

9*x^3+15*x^2-24*x-16 = 0

9*x^3+15*x^2-24*x-16 = 0

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

1

x = 1

9*x^3+15*x^2-24*x-16 = -16

1

-1

x = -1

9*x^3+15*x^2-24*x-16 = 14

-1

2

x = 2

9*x^3+15*x^2-24*x-16 = 68

2

-2

x = -2

9*x^3+15*x^2-24*x-16 = 20

-2

4

x = 4

9*x^3+15*x^2-24*x-16 = 704

4

-4

x = -4

9*x^3+15*x^2-24*x-16 = -256

-4

8

x = 8

9*x^3+15*x^2-24*x-16 = 5360

8

-8

x = -8

9*x^3+15*x^2-24*x-16 = -3472

-8

16

x = 16

9*x^3+15*x^2-24*x-16 = 40304

16

-16

x = -16

9*x^3+15*x^2-24*x-16 = -32656

-16

{ 1/3, -1/3, 1/9, -1/9, -1/3, 1/3, -1/9, 1/9, 2/3, -2/3, 2/9, -2/9, -2/3, 2/3, -2/9, 2/9, 4/3, -4/3, 4/9, -4/9, -4/3, 4/3, -4/9, 4/9, 8/3, -8/3, 8/9, -8/9, -8/3, 8/3, -8/9, 8/9, 16/3, -16/3, 16/9, -16/9, -16/3, 16/3, -16/9, 16/9 }

1/3

x

1/3

9*x^3+15*x^2-24*x-16 = -22

1/3

-1/3

x

-1/3

9*x^3+15*x^2-24*x-16 = -6.66666666

-1/3

1/9

x

1/9

9*x^3+15*x^2-24*x-16 = -18.4691358

1/9

-1/9

x

-1/9

9*x^3+15*x^2-24*x-16 = -13.16049382

-1/9

-1/3

x

-1/3

9*x^3+15*x^2-24*x-16 = -6.66666666

-1/3

1/3

x

1/3

9*x^3+15*x^2-24*x-16 = -22

1/3

-1/9

x

-1/9

9*x^3+15*x^2-24*x-16 = -13.16049382

-1/9

1/9

x

1/9

9*x^3+15*x^2-24*x-16 = -18.4691358

1/9

2/3

x

2/3

9*x^3+15*x^2-24*x-16 = -22.66666666

2/3

-2/3

x

-2/3

9*x^3+15*x^2-24*x-16 = 4

-2/3

2/9

x

2/9

9*x^3+15*x^2-24*x-16 = -20.49382716

2/9

-2/9

x

-2/9

9*x^3+15*x^2-24*x-16 = -10.02469136

-2/9

-2/3

x

-2/3

9*x^3+15*x^2-24*x-16 = 4

-2/3

2/3

x

2/3

9*x^3+15*x^2-24*x-16 = -22.66666666

2/3

-2/9

x

-2/9

9*x^3+15*x^2-24*x-16 = -10.02469136

-2/9

2/9

x

2/9

9*x^3+15*x^2-24*x-16 = -20.49382716

2/9

4/3

x

4/3

9*x^3+15*x^2-24*x-16 = 0

4/3

x-4/3

9*x^2+27*x+12

9*x^3+15*x^2-24*x-16

x-4/3

12*x^2-9*x^3

27*x^2-24*x-16

36*x-27*x^2

12*x-16

16-12*x

0

9*x^2+27*x+12 = 0

DELTA = 27^2-(4*9*12)

DELTA = 297

DELTA > 0

x = (297^(1/2)-27)/(2*9) or x = (-297^(1/2)-27)/(2*9)

x = (3*33^(1/2)-27)/18 or x = (-3*33^(1/2)-27)/18

x in { (-3*33^(1/2)-27)/18, (3*33^(1/2)-27)/18, 4/3} 

(x-((-3*33^(1/2)-27)/18))*(x-((3*33^(1/2)-27)/18))*(x-4/3) = 0

((x-((-3*33^(1/2)-27)/18))*(x-((3*33^(1/2)-27)/18))*(x-4/3))/(3*x-4) = 0

( x-((-3*33^(1/2)-27)/18) )

x-((-3*33^(1/2)-27)/18) = 0 // + (-3*33^(1/2)-27)/18

x = (-3*33^(1/2)-27)/18

( x-((3*33^(1/2)-27)/18) )

x-((3*33^(1/2)-27)/18) = 0 // + (3*33^(1/2)-27)/18

x = (3*33^(1/2)-27)/18

( x-4/3 )

x-4/3 = 0 // + 4/3

x = 4/3

x in { 4/3} 

x in { (-3*33^(1/2)-27)/18, (3*33^(1/2)-27)/18 }

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