# 
restart;
eq1:=a+c+d=0;
eq2:=d*((-1-sqrt(15))^2+4)*(-2*sqrt(15))=13;
eq3:=c*((-1+sqrt(15))^2+4)*(2*sqrt(15))=13;
eq4:=-14*b+4*(1+sqrt(15))*c+4*(1-sqrt(15))*d=13;
solve({eq1,eq2,eq3,eq4},{a,b,c,d});

#