(6x^4-15x^3-17x^2-10x-14)/(3x^2+2)

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Solution for (6x^4-15x^3-17x^2-10x-14)/(3x^2+2) equation: 


D( x )

3*x^2+2 = 0

3*x^2+2 = 0

3*x^2+2 = 0

3*x^2 = -2 // : 3

x^2 = -2/3

x in (-oo:+oo)

(6*x^4-(15*x^3)-(17*x^2)-(10*x)-14)/(3*x^2+2) = 0

(6*x^4-15*x^3-17*x^2-10*x-14)/(3*x^2+2) = 0

6*x^4-15*x^3-17*x^2-10*x-14 = 0

6*x^4-15*x^3-17*x^2-10*x-14 = 0

{ 1, -1, 2, -2, 7, -7, 14, -14 }

1

x = 1

6*x^4-15*x^3-17*x^2-10*x-14 = -50

1

-1

x = -1

6*x^4-15*x^3-17*x^2-10*x-14 = 0

-1

x+1

6*x^3-21*x^2+4*x-14

6*x^4-15*x^3-17*x^2-10*x-14

x+1

-6*x^4-6*x^3

-21*x^3-17*x^2-10*x-14

21*x^3+21*x^2

4*x^2-10*x-14

-4*x^2-4*x

-14*x-14

14*x+14

0

6*x^3-21*x^2+4*x-14 = 0

{ 1, -1, 2, -2, 7, -7, 14, -14 }

1

x = 1

6*x^3-21*x^2+4*x-14 = -25

1

-1

x = -1

6*x^3-21*x^2+4*x-14 = -45

-1

2

x = 2

6*x^3-21*x^2+4*x-14 = -42

2

-2

x = -2

6*x^3-21*x^2+4*x-14 = -154

-2

7

x = 7

6*x^3-21*x^2+4*x-14 = 1043

7

-7

x = -7

6*x^3-21*x^2+4*x-14 = -3129

-7

14

x = 14

6*x^3-21*x^2+4*x-14 = 12390

14

-14

x = -14

6*x^3-21*x^2+4*x-14 = -20650

-14

{ 1/2, -1/2, 1/3, -1/3, 1/6, -1/6, -1/2, 1/2, -1/3, 1/3, -1/6, 1/6, 2/2, -2/2, 2/3, -2/3, 2/6, -2/6, -2/2, 2/2, -2/3, 2/3, -2/6, 2/6, 7/2, -7/2, 7/3, -7/3, 7/6, -7/6, -7/2, 7/2, -7/3, 7/3, -7/6, 7/6, 14/2, -14/2, 14/3, -14/3, 14/6, -14/6, -14/2, 14/2, -14/3, 14/3, -14/6, 14/6 }

1/2

x

1/2

6*x^3-21*x^2+4*x-14 = -16.5

1/2

-1/2

x

-1/2

6*x^3-21*x^2+4*x-14 = -22

-1/2

1/3

x

1/3

6*x^3-21*x^2+4*x-14 = -14.77777778

1/3

-1/3

x

-1/3

6*x^3-21*x^2+4*x-14 = -17.88888888

-1/3

1/6

x

1/6

6*x^3-21*x^2+4*x-14 = -13.88888888

1/6

-1/6

x

-1/6

6*x^3-21*x^2+4*x-14 = -15.27777778

-1/6

-1/2

x

-1/2

6*x^3-21*x^2+4*x-14 = -22

-1/2

1/2

x

1/2

6*x^3-21*x^2+4*x-14 = -16.5

1/2

-1/3

x

-1/3

6*x^3-21*x^2+4*x-14 = -17.88888888

-1/3

1/3

x

1/3

6*x^3-21*x^2+4*x-14 = -14.77777778

1/3

-1/6

x

-1/6

6*x^3-21*x^2+4*x-14 = -15.27777778

-1/6

1/6

x

1/6

6*x^3-21*x^2+4*x-14 = -13.88888888

1/6

2/2

x

2/2

6*x^3-21*x^2+4*x-14 = -25

2/2

-2/2

x

-2/2

6*x^3-21*x^2+4*x-14 = -45

-2/2

2/3

x

2/3

6*x^3-21*x^2+4*x-14 = -18.88888888

2/3

-2/3

x

-2/3

6*x^3-21*x^2+4*x-14 = -27.77777778

-2/3

2/6

x

2/6

6*x^3-21*x^2+4*x-14 = -14.77777778

2/6

-2/6

x

-2/6

6*x^3-21*x^2+4*x-14 = -17.88888888

-2/6

-2/2

x

-2/2

6*x^3-21*x^2+4*x-14 = -45

-2/2

2/2

x

2/2

6*x^3-21*x^2+4*x-14 = -25

2/2

-2/3

x

-2/3

6*x^3-21*x^2+4*x-14 = -27.77777778

-2/3

2/3

x

2/3

6*x^3-21*x^2+4*x-14 = -18.88888888

2/3

-2/6

x

-2/6

6*x^3-21*x^2+4*x-14 = -17.88888888

-2/6

2/6

x

2/6

6*x^3-21*x^2+4*x-14 = -14.77777778

2/6

7/2

x

7/2

6*x^3-21*x^2+4*x-14 = 0

7/2

x-7/2

6*x^2+4

6*x^3-21*x^2+4*x-14

x-7/2

21*x^2-6*x^3

4*x-14

14-4*x

0

6*x^2+4 = 0

DELTA = 0^2-(4*4*6)

DELTA = -96

DELTA < 0

x in { -1, 7/2} 

(x+1)*(x-7/2) = 0

((x+1)*(x-7/2))/(3*x^2+2) = 0

( x+1 )

x+1 = 0 // - 1

x = -1

( x-7/2 )

x-7/2 = 0 // + 7/2

x = 7/2

x in { -1, 7/2 }

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