(1/y)-(1/5y)+(1/y+1)=(5/2y)

Solution for (1/y)-(1/5y)+(1/y+1)=(5/2y) equation:

D( y )

y = 0

y = 0

y = 0

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

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

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

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

2*y^-1-27/10*y^1+1*y^0 = 0

(1*y^1-27/10*y^2+2*y^0)/(y^1) = 0 // * y^2

y^1*(1*y^1-27/10*y^2+2*y^0) = 0

y^1

(-27/10)*y^2+y+2 = 0

(-27/10)*y^2+y+2 = 0

DELTA = 1^2-(2*4*(-27/10))

DELTA = 113/5

DELTA > 0

y = ((113/5)^(1/2)-1)/(2*(-27/10)) or y = (-(113/5)^(1/2)-1)/(2*(-27/10))

y = -5/27*((113/5)^(1/2)-1) or y = 5/27*((113/5)^(1/2)+1)

y in { -5/27*((113/5)^(1/2)-1), 5/27*((113/5)^(1/2)+1)} 

y in { -5/27*((113/5)^(1/2)-1), 5/27*((113/5)^(1/2)+1) }