Question 977415
Hi there,
First of all factorise the equation:-
2x^2 + 9x + 4
(2x + 1)(x + 4)
So, x = -1/2 and x = -4
As this equation is positive (x^2)
it opens upwards.
It will cut the x axis at -4 and go 
down and then rise and cut the x axis at -1/2 
before rising above the x axis.
For 2x^2 + 9x + 4 <0
We are looking at the part of the curve below
the x axis.
This region is defined as:-
-4 < x < -1/2
This is the answer.
 Hope this helps:-)