(5x+4)/x2+3x-10

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Solution for (5x+4)/x2+3x-10 equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

(5*x+4)/(x^2)+3*x-10 = 0

(5*x+4)/(x^2)+(3*x*x^2)/(x^2)+(-10*x^2)/(x^2) = 0

3*x*x^2-10*x^2+5*x+4 = 0

3*x^3-10*x^2+5*x+4 = 0

3*x^3-10*x^2+5*x+4 = 0

3*x^3-10*x^2+5*x+4 = 0

{ 1, -1, 2, -2, 4, -4 }

1

x = 1

3*x^3-10*x^2+5*x+4 = 2

1

-1

x = -1

3*x^3-10*x^2+5*x+4 = -14

-1

2

x = 2

3*x^3-10*x^2+5*x+4 = -2

2

-2

x = -2

3*x^3-10*x^2+5*x+4 = -70

-2

4

x = 4

3*x^3-10*x^2+5*x+4 = 56

4

-4

x = -4

3*x^3-10*x^2+5*x+4 = -368

-4

{ 1/3, -1/3, -1/3, 1/3, 2/3, -2/3, -2/3, 2/3, 4/3, -4/3, -4/3, 4/3 }

1/3

x

1/3

3*x^3-10*x^2+5*x+4 = 4.66666667

1/3

-1/3

x

-1/3

3*x^3-10*x^2+5*x+4 = 1.11111111

-1/3

-1/3

x

-1/3

3*x^3-10*x^2+5*x+4 = 1.11111111

-1/3

1/3

x

1/3

3*x^3-10*x^2+5*x+4 = 4.66666667

1/3

2/3

x

2/3

3*x^3-10*x^2+5*x+4 = 3.77777778

2/3

-2/3

x

-2/3

3*x^3-10*x^2+5*x+4 = -4.66666666

-2/3

-2/3

x

-2/3

3*x^3-10*x^2+5*x+4 = -4.66666666

-2/3

2/3

x

2/3

3*x^3-10*x^2+5*x+4 = 3.77777778

2/3

4/3

x

4/3

3*x^3-10*x^2+5*x+4 = 0

4/3

x-4/3

3*x^2-6*x-3

3*x^3-10*x^2+5*x+4

x-4/3

4*x^2-3*x^3

5*x-6*x^2+4

6*x^2-8*x

4-3*x

3*x-4

0

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

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

DELTA = 72

DELTA > 0

x = (72^(1/2)+6)/(2*3) or x = (6-72^(1/2))/(2*3)

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

x in { (6-6*2^(1/2))/6, (6*2^(1/2)+6)/6, 4/3} 

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

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

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

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

( x-((6*2^(1/2)+6)/6) )

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

x = (6*2^(1/2)+6)/6

( x-((6-6*2^(1/2))/6) )

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

x = (6-6*2^(1/2))/6

( x-4/3 )

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

x = 4/3

x in { (6*2^(1/2)+6)/6, (6-6*2^(1/2))/6, 4/3 }

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