Find the domain of the function $f(x) = \sqrt{6-x-x^2-2x^2}$.
Simplify as
sqrt [ -3x^2 - x + 6 ]
-3x^2 - x + 6 = 0
3x^2 + x - 6 = 0
x = [ -1 - sqrt 73 ] / 6 ≈ -1.59 and x = [ 1 +sqrt 73 ] / 6 ≈ 1.26
The root will be real when x = [ (-1- sqrt 73)/6 , (-1 +sqrt 73)/6 ] = the domain
