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  1. With[{Pt = 0.5, [Sigma] = 0.1, S = 1},
  2.    FindRoot[1/(6 [Sigma]^2 (-1 + w) w) S ((Log[Sqrt[3] [Sigma] + Pt] -
  3.       Log[Pt + Sqrt[3] [Sigma] (1 - 2 w)]) Pt (Sqrt[3] [Sigma] + Pt) - (6 [Sigma]^2 +
  4.        Sqrt[3] [Sigma] (Log[-Sqrt[3] [Sigma] + Pt] + Log[Sqrt[3] [Sigma] + Pt] - 2 Log[Pt + Sqrt[3] [Sigma] (1 - 2 w)]) Pt + (-Log[-Sqrt[
  5.           3] [Sigma] + Pt] + Log[Sqrt[3] [Sigma] + Pt]) Pt^2) w + 6 [Sigma]^2 w^2) == 0, {w, 0.5}]]
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