Question 289509
{{{2x^2 = 3x + 2}}}
{{{f(x)=2x^2 -3x - 2=0}}}
Graph the function the find the x values when it equals zero. 
{{{ graph( 300, 300, -3, 3, -3, 3,  2x^2-3x-2) }}} 
Now looking at the graph, you can guess the x values where f(x)=0. 
Looks like x=2 is one of those points. 
Plug it into the function and check.
{{{f(2)=2(2)^2-3(2)-2=2(4)-6-2=8-6-2=0}}}
x=2 is a root. 
I leave it to you to find the other. 
Guess and check.