we get:
[tex]\begin{gathered} x^2-2x+3=-5x+1\rightarrow \\ x^2+3x-2=0\rightarrow x=\frac{-3+\sqrt[]{17}}{2},x=\frac{-3-\sqrt[]{17}}{2} \end{gathered}[/tex]so the pairs are,
[tex](\frac{-3+\sqrt[]{17}}{2},\frac{15-5\sqrt[]{17}}{2}+1),(\frac{-3-\sqrt[]{17}}{2},\frac{15+5\sqrt[]{17}}{2}+1)[/tex]