Lagrangian Points

Ueff[x_, y_, m1_, x1_, y1_, m2_, x2_, y2_] := 
  -((G*m1)/Sqrt[(x - x1)^2 + (y - y1)^2]) - 
   (G*m2)/Sqrt[(x - x2)^2 + (y - y2)^2] - (G*(m1 + m2)*(x^2 + y^2))/(2*Sqrt[(x1 - x2)^2 + (y1 - y2)^2]^3)
   
G = 1; m1 = 1; x1 = -1.25; y1 = 0; m2 = 0.45; x2 = 1.25; y2 = 0; 
 
L1 = {FindRoot[D[Ueff[x, 0, m1, x1, y1, m2, x2, y2], x], {x, 0.5}][[1,2]], 0}; 
L2 = {FindRoot[D[Ueff[x, 0, m1, x1, y1, m2, x2, y2], x], {x, 1.5}][[1,2]], 0}; 
L3 = {FindRoot[D[Ueff[x, 0, m1, x1, y1, m2, x2, y2], x], {x, -1.5}][[1,2]], 0}; 
L4 = FindRoot[{D[Ueff[x, y, m1, x1, y1, m2, x2, y2], x] == 0, 
      D[Ueff[x, y, m1, x1, y1, m2, x2, y2], y] == 0}, {x, 0.5}, {y, 1}][[All,2]]; 
L5 = FindRoot[{D[Ueff[x, y, m1, x1, y1, m2, x2, y2], x] == 0, 
      D[Ueff[x, y, m1, x1, y1, m2, x2, y2], y] == 0}, {x, 0.5}, {y, -1}][[All,2]]; 
LPts = {L1, L2, L3, L4, L5}; 
LPts3D = Table[Flatten[{LPts[[i]], Ueff[LPts[[i,1]], LPts[[i,2]], m1, x1, y1, m2, x2, y2]}], {i, 1, 5}]; 
 
Show[
    Graphics3D[
      {Darker[Gray, 0.6], Sphere[LPts3D, 0.1], 
       Cyan, Sphere[{x1, y1, -0.85}, m1/2], 
       Magenta, Sphere[{x2, y2, -0.85}, m2/2]}], 
    Plot3D[
      Ueff[x, y, m1, x1, y1, m2, x2, y2], {x, -4, 4}, {y, -4, 4}, 
      PlotRange -> 2, Mesh -> 10, MeshStyle -> Dashed, PlotStyle -> Opacity[0.93], 
      ColorFunction -> ColorData["Rainbow"]], Boxed -> False, Axes -> False]