(2x^3+3x^2-11x-15)/(2x-5)

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Solution for (2x^3+3x^2-11x-15)/(2x-5) equation: 


D( x )

2*x-5 = 0

2*x-5 = 0

2*x-5 = 0

2*x-5 = 0 // + 5

2*x = 5 // : 2

x = 5/2

x in (-oo:5/2) U (5/2:+oo)

(2*x^3+3*x^2-(11*x)-15)/(2*x-5) = 0

(2*x^3+3*x^2-11*x-15)/(2*x-5) = 0

2*x^3+3*x^2-11*x-15 = 0

2*x^3+3*x^2-11*x-15 = 0

{ 1, -1, 3, -3, 5, -5, 15, -15 }

1

x = 1

2*x^3+3*x^2-11*x-15 = -21

1

-1

x = -1

2*x^3+3*x^2-11*x-15 = -3

-1

3

x = 3

2*x^3+3*x^2-11*x-15 = 33

3

-3

x = -3

2*x^3+3*x^2-11*x-15 = -9

-3

5

x = 5

2*x^3+3*x^2-11*x-15 = 255

5

-5

x = -5

2*x^3+3*x^2-11*x-15 = -135

-5

15

x = 15

2*x^3+3*x^2-11*x-15 = 7245

15

-15

x = -15

2*x^3+3*x^2-11*x-15 = -5925

-15

{ 1/2, -1/2, -1/2, 1/2, 3/2, -3/2, -3/2, 3/2, 5/2, -5/2, -5/2, 5/2, 15/2, -15/2, -15/2, 15/2 }

1/2

x

1/2

2*x^3+3*x^2-11*x-15 = -19.5

1/2

-1/2

x

-1/2

2*x^3+3*x^2-11*x-15 = -9

-1/2

-1/2

x

-1/2

2*x^3+3*x^2-11*x-15 = -9

-1/2

1/2

x

1/2

2*x^3+3*x^2-11*x-15 = -19.5

1/2

3/2

x

3/2

2*x^3+3*x^2-11*x-15 = -18

3/2

-3/2

x

-3/2

2*x^3+3*x^2-11*x-15 = 1.5

-3/2

-3/2

x

-3/2

2*x^3+3*x^2-11*x-15 = 1.5

-3/2

3/2

x

3/2

2*x^3+3*x^2-11*x-15 = -18

3/2

5/2

x

5/2

2*x^3+3*x^2-11*x-15 = 7.5

5/2

-5/2

x

-5/2

2*x^3+3*x^2-11*x-15 = 0

-5/2

x+5/2

2*x^2-2*x-6

2*x^3+3*x^2-11*x-15

x+5/2

-2*x^3-5*x^2

-2*x^2-11*x-15

2*x^2+5*x

-6*x-15

6*x+15

0

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

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

DELTA = 52

DELTA > 0

x = (52^(1/2)+2)/(2*2) or x = (2-52^(1/2))/(2*2)

x = (2*13^(1/2)+2)/4 or x = (2-2*13^(1/2))/4

x in { (2-2*13^(1/2))/4, (2*13^(1/2)+2)/4, -5/2} 

(x-((2-2*13^(1/2))/4))*(x-((2*13^(1/2)+2)/4))*(x+5/2) = 0

((x-((2-2*13^(1/2))/4))*(x-((2*13^(1/2)+2)/4))*(x+5/2))/(2*x-5) = 0

( x+5/2 )

x+5/2 = 0 // - 5/2

x = -5/2

( x-((2*13^(1/2)+2)/4) )

x-((2*13^(1/2)+2)/4) = 0 // + (2*13^(1/2)+2)/4

x = (2*13^(1/2)+2)/4

( x-((2-2*13^(1/2))/4) )

x-((2-2*13^(1/2))/4) = 0 // + (2-2*13^(1/2))/4

x = (2-2*13^(1/2))/4

x in { -5/2, (2*13^(1/2)+2)/4, (2-2*13^(1/2))/4 }

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