(1/y-5)+(1/20)=(-3/4y-20)

Solution for (1/y-5)+(1/20)=(-3/4y-20) equation:

D( y )

y = 0

y = 0

y = 0

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

1/y+1/20-5 = (-3/4)*y-20 // - (-3/4)*y-20

1/y-((-3/4)*y)+1/20-5+20 = 0

(3/4)*y+1/y+1/20-5+20 = 0

3/4*y^1+1*y^-1+301/20*y^0 = 0

(3/4*y^2+301/20*y^1+1*y^0)/(y^1) = 0 // * y^2

y^1*(3/4*y^2+301/20*y^1+1*y^0) = 0

y^1

(3/4)*y^2+(301/20)*y+1 = 0

(3/4)*y^2+(301/20)*y+1 = 0

DELTA = (301/20)^2-(1*4*(3/4))

DELTA = 89401/400

DELTA > 0

y = ((89401/400)^(1/2)-(301/20))/(2*(3/4)) or y = (-(301/20)-(89401/400)^(1/2))/(2*(3/4))

y = -1/15 or y = -20

y in { -20, -1/15} 

y in { -20, -1/15 }