(2x^3+5x^2-27x+5)/(2x-5)

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Solution for (2x^3+5x^2-27x+5)/(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+5*x^2-(27*x)+5)/(2*x-5) = 0

(2*x^3+5*x^2-27*x+5)/(2*x-5) = 0

2*x^3+5*x^2-27*x+5 = 0

2*x^3+5*x^2-27*x+5 = 0

{ 1, -1, 5, -5 }

1

x = 1

2*x^3+5*x^2-27*x+5 = -15

1

-1

x = -1

2*x^3+5*x^2-27*x+5 = 35

-1

5

x = 5

2*x^3+5*x^2-27*x+5 = 245

5

-5

x = -5

2*x^3+5*x^2-27*x+5 = 15

-5

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

1/2

x

1/2

2*x^3+5*x^2-27*x+5 = -7

1/2

-1/2

x

-1/2

2*x^3+5*x^2-27*x+5 = 19.5

-1/2

-1/2

x

-1/2

2*x^3+5*x^2-27*x+5 = 19.5

-1/2

1/2

x

1/2

2*x^3+5*x^2-27*x+5 = -7

1/2

5/2

x

5/2

2*x^3+5*x^2-27*x+5 = 0

5/2

x-5/2

2*x^2+10*x-2

2*x^3+5*x^2-27*x+5

x-5/2

5*x^2-2*x^3

10*x^2-27*x+5

25*x-10*x^2

5-2*x

2*x-5

0

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

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

DELTA = 116

DELTA > 0

x = (116^(1/2)-10)/(2*2) or x = (-116^(1/2)-10)/(2*2)

x = (2*29^(1/2)-10)/4 or x = (-2*29^(1/2)-10)/4

x in { (-2*29^(1/2)-10)/4, (2*29^(1/2)-10)/4, 5/2}

(x-((-2*29^(1/2)-10)/4))*(x-((2*29^(1/2)-10)/4))*(x-5/2) = 0

((x-((-2*29^(1/2)-10)/4))*(x-((2*29^(1/2)-10)/4))*(x-5/2))/(2*x-5) = 0

( x-((-2*29^(1/2)-10)/4) )

x-((-2*29^(1/2)-10)/4) = 0 // + (-2*29^(1/2)-10)/4

x = (-2*29^(1/2)-10)/4

( x-((2*29^(1/2)-10)/4) )

x-((2*29^(1/2)-10)/4) = 0 // + (2*29^(1/2)-10)/4

x = (2*29^(1/2)-10)/4

( x-5/2 )

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

x = 5/2

x in { 5/2}

x in { (-2*29^(1/2)-10)/4, (2*29^(1/2)-10)/4 }

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