(12x^3-46x^2-78x-28)/(6x+4)

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Solution for (12x^3-46x^2-78x-28)/(6x+4) equation: 


D( x )

6*x+4 = 0

6*x+4 = 0

6*x+4 = 0

6*x+4 = 0 // - 4

6*x = -4 // : 6

x = -4/6

x = -2/3

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

(12*x^3-(46*x^2)-(78*x)-28)/(6*x+4) = 0

(12*x^3-46*x^2-78*x-28)/(6*x+4) = 0

12*x^3-46*x^2-78*x-28 = 0

2*(6*x^3-23*x^2-39*x-14) = 0

6*x^3-23*x^2-39*x-14 = 0

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

1

x = 1

6*x^3-23*x^2-39*x-14 = -70

1

-1

x = -1

6*x^3-23*x^2-39*x-14 = -4

-1

2

x = 2

6*x^3-23*x^2-39*x-14 = -136

2

-2

x = -2

6*x^3-23*x^2-39*x-14 = -76

-2

7

x = 7

6*x^3-23*x^2-39*x-14 = 644

7

-7

x = -7

6*x^3-23*x^2-39*x-14 = -2926

-7

14

x = 14

6*x^3-23*x^2-39*x-14 = 11396

14

-14

x = -14

6*x^3-23*x^2-39*x-14 = -20440

-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^3-23*x^2-39*x-14 = -38.5

1/2

-1/2

x

-1/2

6*x^3-23*x^2-39*x-14 = -1

-1/2

1/3

x

1/3

6*x^3-23*x^2-39*x-14 = -29.33333334

1/3

-1/3

x

-1/3

6*x^3-23*x^2-39*x-14 = -3.77777778

-1/3

1/6

x

1/6

6*x^3-23*x^2-39*x-14 = -21.11111111

1/6

-1/6

x

-1/6

6*x^3-23*x^2-39*x-14 = -8.16666667

-1/6

-1/2

x

-1/2

6*x^3-23*x^2-39*x-14 = -1

-1/2

1/2

x

1/2

6*x^3-23*x^2-39*x-14 = -38.5

1/2

-1/3

x

-1/3

6*x^3-23*x^2-39*x-14 = -3.77777778

-1/3

1/3

x

1/3

6*x^3-23*x^2-39*x-14 = -29.33333334

1/3

-1/6

x

-1/6

6*x^3-23*x^2-39*x-14 = -8.16666667

-1/6

1/6

x

1/6

6*x^3-23*x^2-39*x-14 = -21.11111111

1/6

2/2

x

2/2

6*x^3-23*x^2-39*x-14 = -70

2/2

-2/2

x

-2/2

6*x^3-23*x^2-39*x-14 = -4

-2/2

2/3

x

2/3

6*x^3-23*x^2-39*x-14 = -48.44444444

2/3

-2/3

x

-2/3

6*x^3-23*x^2-39*x-14 = 0

-2/3

x+2/3

6*x^2-27*x-21

6*x^3-23*x^2-39*x-14

x+2/3

-6*x^3-4*x^2

-27*x^2-39*x-14

27*x^2+18*x

-21*x-14

21*x+14

0

6*x^2-27*x-21 = 0

DELTA = (-27)^2-(-21*4*6)

DELTA = 1233

DELTA > 0

x = (1233^(1/2)+27)/(2*6) or x = (27-1233^(1/2))/(2*6)

x = (3*137^(1/2)+27)/12 or x = (27-3*137^(1/2))/12

x in { (27-3*137^(1/2))/12, (3*137^(1/2)+27)/12, -2/3} 

2*(x-((27-3*137^(1/2))/12))*(x-((3*137^(1/2)+27)/12))*(x+2/3) = 0

(2*(x-((27-3*137^(1/2))/12))*(x-((3*137^(1/2)+27)/12))*(x+2/3))/(6*x+4) = 0

( x+2/3 )

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

x = -2/3

( x-((27-3*137^(1/2))/12) )

x-((27-3*137^(1/2))/12) = 0 // + (27-3*137^(1/2))/12

x = (27-3*137^(1/2))/12

( x-((3*137^(1/2)+27)/12) )

x-((3*137^(1/2)+27)/12) = 0 // + (3*137^(1/2)+27)/12

x = (3*137^(1/2)+27)/12

x in { -2/3} 

x in { (27-3*137^(1/2))/12, (3*137^(1/2)+27)/12 }

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