Here's the "formal" way
Let a and b be the factors
So we have that a * b = 45 divide both sides by b and we have
a = 45/b
And we have that
a + b = 14 sub for a
45/b + b = 14 multiply through by b
45 + b^2 = 14b rearrange
b^2 - 14b + 45 = 0 factor
(b - 9) (b - 5) = 0 setting each factor to 0 we have that b = 9 or b = 5
If b = 9 then a = 45/b = 45/9 = 5
Or.......if b = 5 then a = 45/b = 45/5 = 9
Either way, the two factors are 5 and 9
Hope that helps.....!!!!
