#3q^2 -38q-13=0#
Factorise the quadratic trinomial.
Find factors of #3 and 13# whose products differ by #38#
Note that both #3 and 13# are prime numbers, so there are not many combinations to try.
#" "3 and 13#
#" "darr" "darr#
#" "1" "13" "rarr 3xx13 = 39#
#" "3" "1" "rarr 1 xx 3 rarr = ul1#
#color(white)(xxxxxxxxxxxxxxxxxxx)38larr# the difference
These are the correct factors, now put in the signs:
#" "3 and 13#
#" "darr" "darr#
#" "1" "-13" "rarr 3xx-13 = -39#
#" "3" "+1" "rarr 1 xx +3 rarr = +ul1#
#color(white)(xxxxxxxxxxxxxxxxxxxxxx)-38larr# the difference
#(q-13)(3q+1)=0#
Set each factor equal to #0#
If #q-13=0, rarr q=13#
If #3q+1=0, rarr q = -1/3#