+128408 Note that the discriminant of x^2 + x + 3 = 1^2 - 4(1) (3) = 1 - 12 = -11
This means that this function has no real roots.....and since it's a parabola that turns upward.....then it never intersects the x axis, so it is never < 0 for any value of x
So.....we only need to find the values that make 2x^2 + x - 6 < 0
So
2x^2 + x - 6 < 0 factor the left side
(2x - 3) ( x + 2) < 0
Note that on (inf, -2) this function is > 0
And on ( 3/2 , inf) the same is true
So....it's only < 0 on ( -2, 3/2)
So.....going back to the original function...it must be ≥ 0 on (-inf , -2) U ( 3/2 , inf)
See the graph here : https://www.desmos.com/calculator/agjohh32v6
