How would one go about solving the following inequality in interval notation? 2x^2+x-8>0

Since this expression is quadratic and it's leading coefficient is positive, it must open upwards. Therefore if it has real roots, then the quadratic expression will be positive for x-values greater than those roots. In fact it has the roots: 
 
which is about...
(-oo,-2.26) U (1.76,oo)