vpw = 3.3; 
    Mp = 80; 
    rp = 0.014*Mp; 
    b0 = 26.31016273 - 1.7168*(10^3/t) - 3.5519*Log[t]; 
    b1 = 24.65681838 - 1.547*(10^3/t) - 3.4314*Log[t]; 
    b2 = 9.080370819 - 6.9445*(10^2/t) - 1.2222*Log[t]; 
    g = b0 + b1*phip + b2*phip^2; 
    dg = b1 + 2*b2*phip; 
    ddg = 2*b2; 
    dddg = 0; 

    S1 = 1/(phip*rp*vpw) + 1/(1 - phip) - (2*g - 2*(1 - 2*phip)*dg - 
         phip*(1 - phip)*ddg); 
    S2 = -(1/(phip^2*rp*vpw)) + 1/(1 - phip)^2 - 
        (6*dg - 3*(1 - 2*phip)*ddg - phip*(1 - phip)*dddg); 

       p = Apply[{phip, t} /. FindRoot[{S1 == 0, S2 == 0}, {phip, #1}, {t, #2}] & , 
       {{-2, 400}, {-0.05, 20}, {3, 800}}, {1}]

  {{-1.28734, 414.625}, {-0.0436006, 23.3922}, {2.6102, 820.852}}

    ContourPlot[{S1 == 0, S2 == 0}, {phip, -2, 3}, {t, 0, 1000}, 
      PlotTheme -> "Detailed", PlotPoints -> 100, 
      Epilog -> {Red, PointSize[Large], Point[p]}]

[![Contourplot3][1]][1]


       ContourPlot[{S1 == 0, S2 == 0}, {phip, -0.2, 0.3}, {t, 0, 100}, 
      PlotTheme -> "Detailed", PlotPoints -> 100, 
      Epilog -> {Red, PointSize[Large], Point[p]}]

[![Contourplot4][2]][2]

A question, how can I insert plots here?


  [1]: https://i.stack.imgur.com/BEUj4.gif
  [2]: https://i.stack.imgur.com/cUrR7.gif