(y+5/y^2+2y)-(6/y^2-4)=0

Solution for (y+5/y^2+2y)-(6/y^2-4)=0 equation:

D( y )

y^2 = 0

y^2 = 0

y^2 = 0

1*y^2 = 0 // : 1

y^2 = 0

y = 0

y in (-oo:0) U (0:+oo)

y+2*y+5/(y^2)-(6/(y^2))+4 = 0

y+2*y+5/(y^2)-6*y^-2+4 = 0

3*y^1-1*y^-2+4*y^0 = 0

(3*y^3+4*y^2-1*y^0)/(y^2) = 0 // * y^4

y^2*(3*y^3+4*y^2-1*y^0) = 0

y^2

3*y^3+4*y^2-1 = 0

{ 1, -1 }

1

y = 1

3*y^3+4*y^2-1 = 6

1

-1

y = -1

3*y^3+4*y^2-1 = 0

-1

y+1

3*y^2+y-1

3*y^3+4*y^2-1

y+1

-3*y^3-3*y^2

y^2-1

-y^2-y

-y-1

y+1

0

3*y^2+y-1 = 0

DELTA = 1^2-(-1*3*4)

DELTA = 13

DELTA > 0

y = (13^(1/2)-1)/(2*3) or y = (-13^(1/2)-1)/(2*3)

y = (13^(1/2)-1)/6 or y = (-(13^(1/2)+1))/6

y in { (-(13^(1/2)+1))/6, (13^(1/2)-1)/6, -1} 

y in { (-(13^(1/2)+1))/6, (13^(1/2)-1)/6, -1 }