(4/y)-5=(5/2y)

Solution for (4/y)-5=(5/2y) equation:

D( y )

y = 0

y = 0

y = 0

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

4/y-5 = (5/2)*y // - (5/2)*y

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

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

4*y^-1-5/2*y^1-5*y^0 = 0

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

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

y^1

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

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

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

DELTA = 65

DELTA > 0

y = (65^(1/2)+5)/(2*(-5/2)) or y = (5-65^(1/2))/(2*(-5/2))

y = (65^(1/2)+5)/(-5) or y = (5-65^(1/2))/(-5)

y in { (65^(1/2)+5)/(-5), (5-65^(1/2))/(-5)} 

y in { (65^(1/2)+5)/(-5), (5-65^(1/2))/(-5) }