get four minimization conditions given as $$\begin{aligned}
&&2 (\l_1 + 4 \l_2 + 2 \l_3) v_1 v_2^2  +  2 \l_4 v_2^3  + v_1 (\a_5 v_L^2 + \a_8 v_R^2 + 2 \l_1 v_1^2 - \mu_1^2) +  2 v_2 (\a_4 v_L^2 + \a_7 v_R^2 + 3 \l_4 v_1^2 - \mu_2^2) + M_2 v_L v_R=0, \notag \\
&&2 ( \l_1 v_2 + 3 \l_4 v_1) v_2^2+ v_2 \left\{ (\a_3 + \a_5) v_L^2 + (\a_6 + \a_8) v_R^2  + 2 (\l_1 + 4 \l_2 + 2 \l_3) v_1^2  - \mu_1^2 \right\} + M_1 v_L v_R \notag \\
&& + 2 v_1 ( \a_4 v_L^2+ \a_7 v_R^2 + \l_4 v_1^2 - \mu_2^2) =0, \notag \\
&& \left\{ 4 \a_4 v_1 v_2 + \a_5 v_1^2 + (\a_3 + \a_5) v_2^2  + 2 \b_1  v_L^2+ \b_3 v_R^2 - \mu_4^2\right\}v_L + M_2 v_1 v_R + M_1 v_2 v_R = 0, \notag \\
&& \left\{ 4 \a_7 v_1 v_2 + \a_8 v_1^2 + (\a_6 + \a_8) v_2^2 + 2  \b_2 v_R^2+ \b_3 v_L^2 - \mu_3^2 \right\} v_R + M_2 v_1 v_L + M_1 v_2 v_L =0.\end{aligned}$$

Using these conditions along with the scalar potential, the charged Higgs mass-squared matrix in the gauge basis $({\phi_1^-}^*, \phi_2^+, H_R^+,H_L^+,\delta^+)$ is given as 