x2- 6x +6 =0 compare with ax2 + bx + c = 0
here a = 1; b = -6 ; c = 6;
D = b2 -4ac
= (-6)(-6) - 4 * 1 * 6
= 36 - 24
= 12 [ It is not a perfect square, so, you cannot get roots what u imagined]
Use below method;
x = -b+ square root of D/2a or -b - square root of D/2a
x = - (-6) + square root of 12/ 2*1 or - ( -6) - square root of 12/2*1
x = 6 + 2*square root of 3/2 or 6 - 2* square root of 3/2
x = 3 + square root of 3 or 3 - square root of 3