First you try to factor it:

Multiply 2 by 33, getting 66.  Now we make a column of
ways to factor 66 using two integers:

factors
 1x66
 2x33
 3x22
 6x11


Now since the sign of 66 is positive, we make
a list of the sums:

factors      sums of factors
 1x66          1+66=67    
 2x33          2+33=35 
 3x22          3+22=25
 6x11          6+11=17


Now you try to find one that agrees in absolute value

with the middle term of 



2x^2-24x+33=0



Oh oh!  There aren't any!  So it won't factor. So we 

have to use the quadratic formula.







a=2, b=-24, c=33































Factor 2 out of the top







Divide top and bottom by 2:



 

Edwin