$$ \begin{cases} \left(\frac{1+\sqrt{3}}{2}\right)^2x+\left(\frac{1+\sqrt{3}}{2}\right)y+1=0\\ \left(\frac{1-\sqrt{3}}{2}\right)^2x+\left(\frac{1-\sqrt{3}}{2}\right)y+1=0 \end{cases} $$
I tried setting the equations equal to each other and substituting variables but those methods just made the equation more conplicated.