I need help trying to find the major and minor axis on this problem:

x^2+3y^2-6x+24y+6=0

complete the square to get it into standard form of an ellipse

x^2 - 6x + 9 3(y^2 + 8y + 16) = -6 + 9+48
(x-3)^2 + 3(y+4)^2 = 51
divide by 51
(x-3)^2 /51 + (y+4)^2 / 17 = 1

so a^2 = 51 , a = √51
b^2 = 17 , b = √17

the major axis has length 2a = 2√51
the minor axis has length 2b = 2√17