I have four nonlinear equations I want to find the points of intersection of these equations, and I used the software Mathematica, unfortunately after many hours of waiting it does not give me any result Do you have an idea how to solve this kind of problem?.

My equations are the following

1. (52 \alpha ^2+\alpha (104 \beta +440 \sqrt{3}-1071)+\beta (65 \beta +110 \sqrt{3}-752)-2 (52 \gamma +55 \sqrt{3}-376) \delta +(-52 \gamma -440 \sqrt{3}+1071) \gamma -65 \delta ^2)=0.

2. 52 \alpha ^2+\alpha (-52 \beta +80 \sqrt{3}-450)+2 \beta (13 \beta +10
   

   \sqrt{3}+38)-52 \gamma ^2+\gamma (52 \delta -80 \sqrt{3}+450)-2 \delta (13 \delta +10 \sqrt{3}+38)=0?

3. \beta ^2-\alpha ^3=0.

4. \delta ^2-\gamma ^3=0.