(6u^3-4u^2-3u+2)/(3u^2+u-2)

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Solution for (6u^3-4u^2-3u+2)/(3u^2+u-2) equation: 


D( u )

3*u^2+u-2 = 0

3*u^2+u-2 = 0

3*u^2+u-2 = 0

3*u^2+u-2 = 0

DELTA = 1^2-(-2*3*4)

DELTA = 25

DELTA > 0

u = (25^(1/2)-1)/(2*3) or u = (-25^(1/2)-1)/(2*3)

u = 2/3 or u = -1

u in (-oo:-1) U (-1:2/3) U (2/3:+oo)

(6*u^3-(4*u^2)-(3*u)+2)/(3*u^2+u-2) = 0

(6*u^3-4*u^2-3*u+2)/(3*u^2+u-2) = 0

6*u^3-4*u^2-3*u+2 = 0

6*u^3-4*u^2-3*u+2 = 0

{ 1, -1, 2, -2 }

1

u = 1

6*u^3-4*u^2-3*u+2 = 1

1

-1

u = -1

6*u^3-4*u^2-3*u+2 = -5

-1

2

u = 2

6*u^3-4*u^2-3*u+2 = 28

2

-2

u = -2

6*u^3-4*u^2-3*u+2 = -56

-2

{ 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 }

1/2

u

1/2

6*u^3-4*u^2-3*u+2 = 0.25

1/2

-1/2

u

-1/2

6*u^3-4*u^2-3*u+2 = 1.75

-1/2

1/3

u

1/3

6*u^3-4*u^2-3*u+2 = 0.77777778

1/3

-1/3

u

-1/3

6*u^3-4*u^2-3*u+2 = 2.33333334

-1/3

1/6

u

1/6

6*u^3-4*u^2-3*u+2 = 1.41666667

1/6

-1/6

u

-1/6

6*u^3-4*u^2-3*u+2 = 2.36111111

-1/6

-1/2

u

-1/2

6*u^3-4*u^2-3*u+2 = 1.75

-1/2

1/2

u

1/2

6*u^3-4*u^2-3*u+2 = 0.25

1/2

-1/3

u

-1/3

6*u^3-4*u^2-3*u+2 = 2.33333334

-1/3

1/3

u

1/3

6*u^3-4*u^2-3*u+2 = 0.77777778

1/3

-1/6

u

-1/6

6*u^3-4*u^2-3*u+2 = 2.36111111

-1/6

1/6

u

1/6

6*u^3-4*u^2-3*u+2 = 1.41666667

1/6

2/2

u

2/2

6*u^3-4*u^2-3*u+2 = 1

2/2

-2/2

u

-2/2

6*u^3-4*u^2-3*u+2 = -5

-2/2

2/3

u

2/3

6*u^3-4*u^2-3*u+2 = 0

2/3

u-2/3

6*u^2-3

6*u^3-4*u^2-3*u+2

u-2/3

4*u^2-6*u^3

2-3*u

3*u-2

0

6*u^2-3 = 0

DELTA = 0^2-(-3*4*6)

DELTA = 72

DELTA > 0

u = (72^(1/2)+0)/(2*6) or u = (0-72^(1/2))/(2*6)

u = (2^(1/2))/2 or u = (-2^(1/2))/2

u in { (-2^(1/2))/2, (2^(1/2))/2, 2/3} 

(u-((-2^(1/2))/2))*(u-((2^(1/2))/2))*(u-2/3) = 0

3*u^2+u-2 = 0

3*u^2+u-2 = 0

DELTA = 1^2-(-2*3*4)

DELTA = 25

DELTA > 0

u = (25^(1/2)-1)/(2*3) or u = (-25^(1/2)-1)/(2*3)

u = 2/3 or u = -1

(u+1)*(u-2/3) = 0

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

( u-((-2^(1/2))/2) )

u-((-2^(1/2))/2) = 0 // + (-2^(1/2))/2

u = (-2^(1/2))/2

( u-((2^(1/2))/2) )

u-((2^(1/2))/2) = 0 // + (2^(1/2))/2

u = (2^(1/2))/2

( u-2/3 )

u-2/3 = 0 // + 2/3

u = 2/3

u in { 2/3} 

u in { (-2^(1/2))/2, (2^(1/2))/2 }

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