Solve[ϵ x^2 + x - 1==0,x]

Manipulate[Solve[ϵ x^2 + x - 1==0,x],{{ϵ,1},0,1}]

Manipulate[Plot[ϵ x^2 + x - 1, {x,-10,3}],{{ϵ,1},0,1}]