(y^2-25)/(2y^2-8y-10)=y

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Solution for (y^2-25)/(2y^2-8y-10)=y equation: 


D( y )

2*y^2-(8*y)-10 = 0

2*y^2-(8*y)-10 = 0

2*y^2-(8*y)-10 = 0

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

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

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

DELTA = 144

DELTA > 0

y = (144^(1/2)+8)/(2*2) or y = (8-144^(1/2))/(2*2)

y = 5 or y = -1

y in (-oo:-1) U (-1:5) U (5:+oo)

(y^2-25)/(2*y^2-(8*y)-10) = y // - y

(y^2-25)/(2*y^2-(8*y)-10)-y = 0

(y^2-25)/(2*y^2-8*y-10)-y = 0

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

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

2*(y^2-4*y-5) = 0

y^2-4*y-5 = 0

DELTA = (-4)^2-(-5*1*4)

DELTA = 36

DELTA > 0

y = (36^(1/2)+4)/(1*2) or y = (4-36^(1/2))/(1*2)

y = 5 or y = -1

2*(y+1)*(y-5) = 0

(y^2-25)/(2*(y+1)*(y-5))-y = 0

(y^2-25)/(2*(y+1)*(y-5))+(2*(-y)*(y+1)*(y-5))/(2*(y+1)*(y-5)) = 0

2*(-y)*(y+1)*(y-5)+y^2-25 = 0

9*y^2-2*y^3+10*y-25 = 0

9*y^2-2*y^3+10*y-25 = 0

9*y^2-2*y^3+10*y-25 = 0

{ 1, -1, 5, -5, 25, -25 }

1

y = 1

9*y^2-2*y^3+10*y-25 = -8

1

-1

y = -1

9*y^2-2*y^3+10*y-25 = -24

-1

5

y = 5

9*y^2-2*y^3+10*y-25 = 0

5

y-5

5-2*y^2-y

9*y^2-2*y^3+10*y-25

y-5

2*y^3-10*y^2

10*y-y^2-25

y^2-5*y

5*y-25

25-5*y

0

5-2*y^2-y = 0

DELTA = (-1)^2-(-2*4*5)

DELTA = 41

DELTA > 0

y = (41^(1/2)+1)/(-2*2) or y = (1-41^(1/2))/(-2*2)

y = (41^(1/2)+1)/(-4) or y = (1-41^(1/2))/(-4)

y in { (41^(1/2)+1)/(-4), (1-41^(1/2))/(-4), 5} 

(y-((41^(1/2)+1)/(-4)))*(y-((1-41^(1/2))/(-4)))*(y-5) = 0

((y-((41^(1/2)+1)/(-4)))*(y-((1-41^(1/2))/(-4)))*(y-5))/(2*(y+1)*(y-5)) = 0

((y-((41^(1/2)+1)/(-4)))*(y-((1-41^(1/2))/(-4)))*(y-5))/(2*(y+1)*(y-5)) = 0 // * 2*(y+1)*(y-5)

(y-((41^(1/2)+1)/(-4)))*(y-((1-41^(1/2))/(-4)))*(y-5) = 0

( y-((1-41^(1/2))/(-4)) )

y-((1-41^(1/2))/(-4)) = 0 // + (1-41^(1/2))/(-4)

y = (1-41^(1/2))/(-4)

( y-((41^(1/2)+1)/(-4)) )

y-((41^(1/2)+1)/(-4)) = 0 // + (41^(1/2)+1)/(-4)

y = (41^(1/2)+1)/(-4)

( y-5 )

y-5 = 0 // + 5

y = 5

y in { 5} 

y in { (1-41^(1/2))/(-4), (41^(1/2)+1)/(-4) }

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