circle

2x^2 + 2y^2 + 4x + 12y + 6 = 0     Divide by 2

x^2 + 2x       + y^2 + 6y    = -6        'Complete the square' for x and y

(x+1)²           + (y+3)²       = -6 + 2 + 9  = 5              5 is radius²      radius = sqrt 5

                          center is (-1,-3)