(8x^3+2x^2-25x-15)/(2x+3)

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Solution for (8x^3+2x^2-25x-15)/(2x+3) equation: 


D( x )

2*x+3 = 0

2*x+3 = 0

2*x+3 = 0

2*x+3 = 0 // - 3

2*x = -3 // : 2

x = -3/2

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

(8*x^3+2*x^2-(25*x)-15)/(2*x+3) = 0

(8*x^3+2*x^2-25*x-15)/(2*x+3) = 0

8*x^3+2*x^2-25*x-15 = 0

8*x^3+2*x^2-25*x-15 = 0

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

1

x = 1

8*x^3+2*x^2-25*x-15 = -30

1

-1

x = -1

8*x^3+2*x^2-25*x-15 = 4

-1

3

x = 3

8*x^3+2*x^2-25*x-15 = 144

3

-3

x = -3

8*x^3+2*x^2-25*x-15 = -138

-3

5

x = 5

8*x^3+2*x^2-25*x-15 = 910

5

-5

x = -5

8*x^3+2*x^2-25*x-15 = -840

-5

15

x = 15

8*x^3+2*x^2-25*x-15 = 27060

15

-15

x = -15

8*x^3+2*x^2-25*x-15 = -26190

-15

{ 1/2, -1/2, 1/4, -1/4, 1/8, -1/8, -1/2, 1/2, -1/4, 1/4, -1/8, 1/8, 3/2, -3/2, 3/4, -3/4, 3/8, -3/8, -3/2, 3/2, -3/4, 3/4, -3/8, 3/8, 5/2, -5/2, 5/4, -5/4, 5/8, -5/8, -5/2, 5/2, -5/4, 5/4, -5/8, 5/8, 15/2, -15/2, 15/4, -15/4, 15/8, -15/8, -15/2, 15/2, -15/4, 15/4, -15/8, 15/8 }

1/2

x

1/2

8*x^3+2*x^2-25*x-15 = -26

1/2

-1/2

x

-1/2

8*x^3+2*x^2-25*x-15 = -3

-1/2

1/4

x

1/4

8*x^3+2*x^2-25*x-15 = -21

1/4

-1/4

x

-1/4

8*x^3+2*x^2-25*x-15 = -8.75

-1/4

1/8

x

1/8

8*x^3+2*x^2-25*x-15 = -18.078125

1/8

-1/8

x

-1/8

8*x^3+2*x^2-25*x-15 = -11.859375

-1/8

-1/2

x

-1/2

8*x^3+2*x^2-25*x-15 = -3

-1/2

1/2

x

1/2

8*x^3+2*x^2-25*x-15 = -26

1/2

-1/4

x

-1/4

8*x^3+2*x^2-25*x-15 = -8.75

-1/4

1/4

x

1/4

8*x^3+2*x^2-25*x-15 = -21

1/4

-1/8

x

-1/8

8*x^3+2*x^2-25*x-15 = -11.859375

-1/8

1/8

x

1/8

8*x^3+2*x^2-25*x-15 = -18.078125

1/8

3/2

x

3/2

8*x^3+2*x^2-25*x-15 = -21

3/2

-3/2

x

-3/2

8*x^3+2*x^2-25*x-15 = 0

-3/2

x+3/2

8*x^2-10*x-10

8*x^3+2*x^2-25*x-15

x+3/2

-8*x^3-12*x^2

-10*x^2-25*x-15

10*x^2+15*x

-10*x-15

10*x+15

0

8*x^2-10*x-10 = 0

DELTA = (-10)^2-(-10*4*8)

DELTA = 420

DELTA > 0

x = (420^(1/2)+10)/(2*8) or x = (10-420^(1/2))/(2*8)

x = (2*105^(1/2)+10)/16 or x = (10-2*105^(1/2))/16

x in { (10-2*105^(1/2))/16, (2*105^(1/2)+10)/16, -3/2} 

(x-((10-2*105^(1/2))/16))*(x-((2*105^(1/2)+10)/16))*(x+3/2) = 0

((x-((10-2*105^(1/2))/16))*(x-((2*105^(1/2)+10)/16))*(x+3/2))/(2*x+3) = 0

( x+3/2 )

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

x = -3/2

( x-((10-2*105^(1/2))/16) )

x-((10-2*105^(1/2))/16) = 0 // + (10-2*105^(1/2))/16

x = (10-2*105^(1/2))/16

( x-((2*105^(1/2)+10)/16) )

x-((2*105^(1/2)+10)/16) = 0 // + (2*105^(1/2)+10)/16

x = (2*105^(1/2)+10)/16

x in { -3/2} 

x in { (10-2*105^(1/2))/16, (2*105^(1/2)+10)/16 }

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