domain

Simplify as

sqrt [ -3x^2 - x + 6 ] 

The expression under the root  must be  ≥ 0   (we can't take the sq rt  of a  negative)

So

-3x^2 - x +  6  ≥  0

This is a  parabola that opens  downward......all we have to  do is to  find the  roots....the domain will lie  between these roots an also include them....so...

-3x^2  - x  + 6 = 0         multiply through by -1

3x^2 + x - 6 =  0

By the quadratic formula

x =   [ -1 - sqrt [ 1^2 - 4*3* -6 ]/ [ 2 *3 ] =   [ -1 - sqrt ( 73 ) ] / 6

and

x =  [ -1 + sqrt (73) ]  6

So....the domain  is

[    (-1 -sqrt 73) / 6  ,  (-1 + sqrt 73) / 6    ]