t1[x_] := 77.4 + 25.27*x - 33.66*x^2 + 51.52*x^3 - 42.65*x^4 + 12.32*x^5;

t2[x_] := 77.4 + 8.372*x - 6.162*x^2 + 14.62*x^3 + 2.201*x^4 - 6.235*x^5;

p1 = Plot[{t1[x], t2[x]}, {x, 0, 1}, Frame -> True, PlotRange -> {{0, 1}, {76, 92}},
   PlotLegends -> "Expressions", ImageSize -> Large]


no = 40*0.21;
nn = 40*0.79;

xg = FindRoot[t1[x] == 78, {x, 1}];
xl = FindRoot[t2[x] == 83, {x, 1}];


sol = Flatten[Thread[Solve[{xg == ngo/(ngn + ngo), xl == nlo/(nln + nlo),
      no == ngo + nlo, nn == ngn + nln}, {ngo, nlo, ngn, nln}, Reals]]]


p2 = Graphics[Point[{ngo, nlo, ngn, nln}]]
p3 = ListPlot[{ngo, nlo, ngn, nln}]
Show[p1, p2, p3]