Question 1074755
{{{2x^2-3x-2>0}}}
{{{(2x+1)(x-2)>0}}}
So the critical points (zeros) are:
{{{2x+1=0}}}
{{{2x=-1}}}
{{{x=-1/2}}}
and
{{{x-2=0}}}
{{{x=2}}}
Break up the number line using these critical values.
Region 1: ({{{-infinity}}},{{{-1/2}}})
Region 2: ({{{-1/2}}},{{{2}}})
Region 3: ({{{2}}},{{{-infinity}}})
Test the inequality in each region to see if it's part of the solution set.
I'll do the first region and you finish it.
Region 1: ({{{-infinity}}},{{{-1/2}}})
CHoose a point in the region, not an endpoint,
{{{x=-1}}}
Test the inequality,
{{{2x^2> 3x+2}}}
{{{2(-1)^2>3(-1)+2}}}
{{{2(1)>-3+2}}}
{{{2>-1}}}
True so region 1 is part of the solution set. 
Continue and test the other two regions.