(28x-2)/(2x^2+7x-30)+(x-5)/(5-2x)+(3x+8)/(x+6)

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Solution for (28x-2)/(2x^2+7x-30)+(x-5)/(5-2x)+(3x+8)/(x+6) equation: 


D( x )

5-(2*x) = 0

x+6 = 0

2*x^2+7*x-30 = 0

5-(2*x) = 0

5-(2*x) = 0

5-2*x = 0

5-2*x = 0 // - 5

-2*x = -5 // : -2

x = -5/(-2)

x = 5/2

x+6 = 0

x+6 = 0

x+6 = 0 // - 6

x = -6

2*x^2+7*x-30 = 0

2*x^2+7*x-30 = 0

2*x^2+7*x-30 = 0

DELTA = 7^2-(-30*2*4)

DELTA = 289

DELTA > 0

x = (289^(1/2)-7)/(2*2) or x = (-289^(1/2)-7)/(2*2)

x = 5/2 or x = -6

x in (-oo:-6) U (-6:5/2) U (5/2:+oo)

(28*x-2)/(2*x^2+7*x-30)+(x-5)/(5-(2*x))+(3*x+8)/(x+6) = 0

(28*x-2)/(2*x^2+7*x-30)+(x-5)/(5-2*x)+(3*x+8)/(x+6) = 0

2*x^2+7*x-30 = 0

2*x^2+7*x-30 = 0

2*x^2+7*x-30 = 0

DELTA = 7^2-(-30*2*4)

DELTA = 289

DELTA > 0

x = (289^(1/2)-7)/(2*2) or x = (-289^(1/2)-7)/(2*2)

x = 5/2 or x = -6

(x+6)*(x-5/2) = 0

(28*x-2)/((x+6)*(x-5/2))+(x-5)/(5-2*x)+(3*x+8)/(x+6) = 0

((28*x-2)*(5-2*x))/((x+6)*(x-5/2)*(5-2*x))+((x-5)*(x+6)*(x-5/2))/((x+6)*(x-5/2)*(5-2*x))+((3*x+8)*(x-5/2)*(5-2*x))/((x+6)*(x-5/2)*(5-2*x)) = 0

(28*x-2)*(5-2*x)+(x-5)*(x+6)*(x-5/2)+(3*x+8)*(x-5/2)*(5-2*x) = 0

x^3-6*x^3-115/2*x^2+14*x^2+223/2*x+85/2*x-100+65 = 0

154*x-5*x^3-87/2*x^2-35 = 0

154*x-5*x^3-87/2*x^2-35 = 0

(-87/2)*x^2-5*x^3+154*x-35 = 0

(-87/2)*x^2-5*x^3+154*x-35 = 0 // * 0

{ 1, -1, 2, -2, 5, -5, 7, -7, 10, -10, 14, -14, 35, -35, 70, -70 }

1

x = 1

308*x-10*x^3-87*x^2-70 = 141

1

-1

x = -1

308*x-10*x^3-87*x^2-70 = -455

-1

2

x = 2

308*x-10*x^3-87*x^2-70 = 118

2

-2

x = -2

308*x-10*x^3-87*x^2-70 = -954

-2

5

x = 5

308*x-10*x^3-87*x^2-70 = -1955

5

-5

x = -5

308*x-10*x^3-87*x^2-70 = -2535

-5

7

x = 7

308*x-10*x^3-87*x^2-70 = -5607

7

-7

x = -7

308*x-10*x^3-87*x^2-70 = -3059

-7

10

x = 10

308*x-10*x^3-87*x^2-70 = -15690

10

-10

x = -10

308*x-10*x^3-87*x^2-70 = -1850

-10

14

x = 14

308*x-10*x^3-87*x^2-70 = -40250

14

-14

x = -14

308*x-10*x^3-87*x^2-70 = 6006

-14

35

x = 35

308*x-10*x^3-87*x^2-70 = -524615

35

-35

x = -35

308*x-10*x^3-87*x^2-70 = 311325

-35

70

x = 70

308*x-10*x^3-87*x^2-70 = -3834810

70

-70

x = -70

308*x-10*x^3-87*x^2-70 = 2982070

-70

{ 1/2, -1/2, 1/5, -1/5, 1/10, -1/10, -1/2, 1/2, -1/5, 1/5, -1/10, 1/10, 2/2, -2/2, 2/5, -2/5, 2/10, -2/10, -2/2, 2/2, -2/5, 2/5, -2/10, 2/10, 5/2, -5/2, 5/5, -5/5, 5/10, -5/10, -5/2, 5/2, -5/5, 5/5, -5/10, 5/10, 7/2, -7/2, 7/5, -7/5, 7/10, -7/10, -7/2, 7/2, -7/5, 7/5, -7/10, 7/10, 10/2, -10/2, 10/5, -10/5, 10/10, -10/10, -10/2, 10/2, -10/5, 10/5, -10/10, 10/10, 14/2, -14/2, 14/5, -14/5, 14/10, -14/10, -14/2, 14/2, -14/5, 14/5, -14/10, 14/10, 35/2, -35/2, 35/5, -35/5, 35/10, -35/10, -35/2, 35/2, -35/5, 35/5, -35/10, 35/10, 70/2, -70/2, 70/5, -70/5, 70/10, -70/10, -70/2, 70/2, -70/5, 70/5, -70/10, 70/10 }

1/2

x

1/2

308*x-10*x^3-87*x^2-70 = 61

1/2

-1/2

x

-1/2

308*x-10*x^3-87*x^2-70 = -244.5

-1/2

1/5

x

1/5

308*x-10*x^3-87*x^2-70 = -11.96

1/5

-1/5

x

-1/5

308*x-10*x^3-87*x^2-70 = -135

-1/5

1/10

x

1/10

308*x-10*x^3-87*x^2-70 = -40.08

1/10

-1/10

x

-1/10

308*x-10*x^3-87*x^2-70 = -101.66

-1/10

-1/2

x

-1/2

308*x-10*x^3-87*x^2-70 = -244.5

-1/2

1/2

x

1/2

308*x-10*x^3-87*x^2-70 = 61

1/2

-1/5

x

-1/5

308*x-10*x^3-87*x^2-70 = -135

-1/5

1/5

x

1/5

308*x-10*x^3-87*x^2-70 = -11.96

1/5

-1/10

x

-1/10

308*x-10*x^3-87*x^2-70 = -101.66

-1/10

1/10

x

1/10

308*x-10*x^3-87*x^2-70 = -40.08

1/10

2/2

x

2/2

308*x-10*x^3-87*x^2-70 = 141

2/2

-2/2

x

-2/2

308*x-10*x^3-87*x^2-70 = -455

-2/2

2/5

x

2/5

308*x-10*x^3-87*x^2-70 = 38.64

2/5

-2/5

x

-2/5

308*x-10*x^3-87*x^2-70 = -206.48

-2/5

2/10

x

2/10

308*x-10*x^3-87*x^2-70 = -11.96

2/10

-2/10

x

-2/10

308*x-10*x^3-87*x^2-70 = -135

-2/10

-2/2

x

-2/2

308*x-10*x^3-87*x^2-70 = -455

-2/2

2/2

x

2/2

308*x-10*x^3-87*x^2-70 = 141

2/2

-2/5

x

-2/5

308*x-10*x^3-87*x^2-70 = -206.48

-2/5

2/5

x

2/5

308*x-10*x^3-87*x^2-70 = 38.64

2/5

-2/10

x

-2/10

308*x-10*x^3-87*x^2-70 = -135

-2/10

2/10

x

2/10

308*x-10*x^3-87*x^2-70 = -11.96

2/10

5/2

x

5/2

308*x-10*x^3-87*x^2-70 = 0

5/2

x-5/2

28-10*x^2-112*x

308*x-10*x^3-87*x^2-70

x-5/2

10*x^3-25*x^2

308*x-112*x^2-70

112*x^2-280*x

28*x-70

70-28*x

0

28-10*x^2-112*x = 0

DELTA = (-112)^2-(-10*4*28)

DELTA = 13664

DELTA > 0

x = (13664^(1/2)+112)/(-10*2) or x = (112-13664^(1/2))/(-10*2)

x = (4*854^(1/2)+112)/(-20) or x = (112-4*854^(1/2))/(-20)

x in { (4*854^(1/2)+112)/(-20), (112-4*854^(1/2))/(-20), 5/2} 

(x-((4*854^(1/2)+112)/(-20)))*(x-((112-4*854^(1/2))/(-20)))*(x-5/2) = 0

((x-((4*854^(1/2)+112)/(-20)))*(x-((112-4*854^(1/2))/(-20)))*(x-5/2))/((x+6)*(x-5/2)*(5-2*x)) = 0

((x-((4*854^(1/2)+112)/(-20)))*(x-((112-4*854^(1/2))/(-20)))*(x-5/2))/((x+6)*(x-5/2)*(5-2*x)) = 0 // * (x+6)*(x-5/2)*(5-2*x)

(x-((4*854^(1/2)+112)/(-20)))*(x-((112-4*854^(1/2))/(-20)))*(x-5/2) = 0

( x-((112-4*854^(1/2))/(-20)) )

x-((112-4*854^(1/2))/(-20)) = 0 // + (112-4*854^(1/2))/(-20)

x = (112-4*854^(1/2))/(-20)

( x-((4*854^(1/2)+112)/(-20)) )

x-((4*854^(1/2)+112)/(-20)) = 0 // + (4*854^(1/2)+112)/(-20)

x = (4*854^(1/2)+112)/(-20)

( x-5/2 )

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

x = 5/2

x in { 5/2} 

x in { (112-4*854^(1/2))/(-20), (4*854^(1/2)+112)/(-20) }

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