$\displaystyle \begin{array}{{>{\displaystyle}l}} x^{2} +3y^{2} -4x+6y+7=0\ \\ x^{2} -4x+4+3\left( y^{2} +2y+1\right) =0\ \\ ( x-2)^{2} +3( y+1)^{2} =0\ \\ \rightarrow \begin{cases} x-2=0 & \\ y+1=0 & \end{cases}\rightarrow \begin{cases} x=2 & \\ y=-1 & \end{cases} \end{array}$