Plot[{(Sqrt[12 (π^2) - ϵ]), (Sqrt[ϵ]) Tan[(Sqrt[ϵ])]}, {ϵ, 0, 125},PlotRange -> {{0,125},{-5, 12}}, AxesLabel -> Automatic]

FindRoot[(Sqrt[12 (π^2) -ϵ])-(Sqrt[ϵ]) Tan[(Sqrt[ϵ])] == 0,{ϵ, {1, 15, 50, 90}}]

Plot[{(Sqrt[12 (π^2) - ϵ]), -(Sqrt[ϵ])  Cot[(Sqrt[ϵ])]}, {ϵ, 0, 125}, PlotRange -> {{0, 125},{-5, 12}}, AxesLabel -> Automatic]

FindRoot[(Sqrt[12 (π^2) -ϵ])+ (Sqrt[ϵ]) Cot[(Sqrt[ϵ])] == 0,{ϵ, {5, 30, 70}}]