Solution for the Critical Isotherm from Van Der Waals Equation

At critical temperature \[T_c\], and critical Pressure \[P_c\], the Van Der Waals Equation has exactly one solution for the critical molar volume \[\bar{V}_c\] \[ \Rightarrow \bar{V}_c-(b+\frac{RT_c}{P_c})\bar{{V}_c}^2+\frac{a}{p}\bar{V}_c-\frac{ab}{P_c}=(\bar{V}-\bar{V}_c)^3 \\ \] \[\Rightarrow \bar{V}_c=3b, P_c=\frac{a}{27b^2}, T_c=\frac{8a}{27bR} \]