8y-1/3=5/y

Solution for 8y-1/3=5/y equation:

D( y )

y = 0

y = 0

y = 0

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

8*y-(1/3) = 5/y // - 5/y

8*y-(5/y)-(1/3) = 0

8*y-5*y^-1-1/3 = 0

8*y^1-5*y^-1-1/3*y^0 = 0

(8*y^2-1/3*y^1-5*y^0)/(y^1) = 0 // * y^2

y^1*(8*y^2-1/3*y^1-5*y^0) = 0

y^1

8*y^2+(-1/3)*y-5 = 0

8*y^2+(-1/3)*y-5 = 0

DELTA = (-1/3)^2-(-5*4*8)

DELTA = 1441/9

DELTA > 0

y = ((1441/9)^(1/2)-(-1/3))/(2*8) or y = (-(-1/3)-(1441/9)^(1/2))/(2*8)

y = ((1441/9)^(1/2)+1/3)/16 or y = (1/3-(1441/9)^(1/2))/16

y in { (1/3-(1441/9)^(1/2))/16, ((1441/9)^(1/2)+1/3)/16} 

y in { (1/3-(1441/9)^(1/2))/16, ((1441/9)^(1/2)+1/3)/16 }