Shuldn't it be y = 3x^2+12x+11

well won't +11 be the y-intercept (y-intercept is when x=0, 0 + 0 + 11 = 11, y-intercept therfore = 11!!)

and as you simplified it to

3(x+2)^2-1

the x-intercept is attained when y = 0 , so when y = 0

0 = 3(x+2)^2-1

1 = 3(x+2)^2

1/3 = (x+2)^2

+-sqrt (1/3) = x + 2 (square root of a number can have a positive value or a negative value)

x = +-sqrt (1/3) - 2

PS +- = plus or minus, when written they usualy go under one another, but the computer can't do that for me