(y-1/6y)-(1/4)=1/y

Solution for (y-1/6y)-(1/4)=1/y equation:

D( y )

y = 0

y = 0

y = 0

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

y-((1/6)*y)-(1/4) = 1/y // - 1/y

y-((1/6)*y)-(1/y)-(1/4) = 0

y+(-1/6)*y-y^-1-1/4 = 0

5/6*y^1-1*y^-1-1/4*y^0 = 0

(5/6*y^2-1/4*y^1-1*y^0)/(y^1) = 0 // * y^2

y^1*(5/6*y^2-1/4*y^1-1*y^0) = 0

y^1

(5/6)*y^2+(-1/4)*y-1 = 0

(5/6)*y^2+(-1/4)*y-1 = 0

DELTA = (-1/4)^2-(-1*4*(5/6))

DELTA = 163/48

DELTA > 0

y = ((163/48)^(1/2)-(-1/4))/(2*(5/6)) or y = (-(-1/4)-(163/48)^(1/2))/(2*(5/6))

y = 3/5*((163/48)^(1/2)+1/4) or y = 3/5*(1/4-(163/48)^(1/2))

y in { 3/5*(1/4-(163/48)^(1/2)), 3/5*((163/48)^(1/2)+1/4)} 

y in { 3/5*(1/4-(163/48)^(1/2)), 3/5*((163/48)^(1/2)+1/4) }