(4/5y)+(y-2)/y=-1/5

Solution for (4/5y)+(y-2)/y=-1/5 equation:

D( y )

y = 0

y = 0

y = 0

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

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

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

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

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

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

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

4*y^2+5*y+y-10 = 0

4*y^2+6*y-10 = 0

4*y^2+6*y-10 = 0

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

2*y^2+3*y-5 = 0

DELTA = 3^2-(-5*2*4)

DELTA = 49

DELTA > 0

y = (49^(1/2)-3)/(2*2) or y = (-49^(1/2)-3)/(2*2)

y = 1 or y = -5/2

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

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

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

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

( y+5/2 )

y+5/2 = 0 // - 5/2

y = -5/2

( y-1 )

y-1 = 0 // + 1

y = 1

y in { -5/2, 1 }