Question 715227
let's get this into shape!
rearranging the equation gives {{{2x^2+7x-9=0}}}
Now we look for factor pairs of the constant term i.e. 9
the factor pairs of -9 are
plus/minus 3 and plus minus 3
plus/minus 1 and plus/minus 9
given that the squared term coefficient is 2 and we have to add these factors to make the linear term's coefficient
the factor pair we will use is plus/minus 1 and plus/minus 9
because +9 + 2(-1) = +7
giving us
(2x+9)(x-1)=0
either of these could =0
so we have
2x+9=0 OR x-1=0
giving us 
{{{x=-9/2}}} OR x=1
CHECK
{{{2(-9/2)^2+7(-9/2)}}}={{{162/4-63/2}}}=9
OR
{{{2(1)^2+7(1)}}}=9
both our solutions are correct!