(6x^3-5x^2-4x+3)/x-1

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Solution for (6x^3-5x^2-4x+3)/x-1 equation:


D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

(6*x^3-(5*x^2)-(4*x)+3)/x-1 = 0

(6*x^3-5*x^2-4*x+3)/x-1 = 0

(6*x^3-5*x^2-4*x+3)/x+(-1*x)/x = 0

6*x^3-5*x^2-4*x-1*x+3 = 0

6*x^3-5*x^2-5*x+3 = 0

6*x^3-5*x^2-5*x+3 = 0

6*x^3-5*x^2-5*x+3 = 0

{ 1, -1, 3, -3 }

1

x = 1

6*x^3-5*x^2-5*x+3 = -1

1

-1

x = -1

6*x^3-5*x^2-5*x+3 = -3

-1

3

x = 3

6*x^3-5*x^2-5*x+3 = 105

3

-3

x = -3

6*x^3-5*x^2-5*x+3 = -189

-3

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

1/2

x

1/2

6*x^3-5*x^2-5*x+3 = 0

1/2

x-1/2

6*x^2-2*x-6

6*x^3-5*x^2-5*x+3

x-1/2

3*x^2-6*x^3

3-2*x^2-5*x

2*x^2-x

3-6*x

6*x-3

0

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

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

DELTA = 148

DELTA > 0

x = (148^(1/2)+2)/(2*6) or x = (2-148^(1/2))/(2*6)

x = (2*37^(1/2)+2)/12 or x = (2-2*37^(1/2))/12

x in { (2-2*37^(1/2))/12, (2*37^(1/2)+2)/12, 1/2}

(x-((2-2*37^(1/2))/12))*(x-((2*37^(1/2)+2)/12))*(x-1/2) = 0

((x-((2-2*37^(1/2))/12))*(x-((2*37^(1/2)+2)/12))*(x-1/2))/x = 0

((x-((2-2*37^(1/2))/12))*(x-((2*37^(1/2)+2)/12))*(x-1/2))/x = 0 // * x

(x-((2-2*37^(1/2))/12))*(x-((2*37^(1/2)+2)/12))*(x-1/2) = 0

( x-((2*37^(1/2)+2)/12) )

x-((2*37^(1/2)+2)/12) = 0 // + (2*37^(1/2)+2)/12

x = (2*37^(1/2)+2)/12

( x-((2-2*37^(1/2))/12) )

x-((2-2*37^(1/2))/12) = 0 // + (2-2*37^(1/2))/12

x = (2-2*37^(1/2))/12

( x-1/2 )

x-1/2 = 0 // + 1/2

x = 1/2

x in { (2*37^(1/2)+2)/12, (2-2*37^(1/2))/12, 1/2 }

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