Question: missing results when solving 3 equations with 3 variables

Hello,I'm trying to solve system of 3 equations for a problem of using Larrange Multiplier

> e1 := 3*x^2+3*y-a*(2*x-6);
             
                          3 x  + 3 y - a (2 x - 6)
> e2 := 3*y^2+3*x-a*(2*y-6);

           
                          3 y  + 3 x - a (2 y - 6)
> e3 := x^2+y^2-6*x-6*y+9;    

                           x  + y  - 6 x - 6 y + 9
I tried to use fsolve but it only return

> fsolve({e1, e2, e3});
           {a = -1.167261890, x = 0.8786796564, y = 0.8786796564}

But there are 1 more (x,y) which is approximately (5.12,5.12)

I also tried solve and then evalf,the 1st (x,y) was right,but the second was something like this

x = 6.41547595 - 2.676840659 *I,

                                       y = 6.415475947 + 2.676840665 * I

Thanks for any help.