This post is not attached to anything. If you repost this with a picture I can try to answer your question.
We know that
if the bird flies 5/6 miles north for -------------> 3/8 miles east
then
for 1 mile north------------------------------> X miles east?
X=(3/8)/(5/6)-------> 18/40-------> 9/20 miles
the answer is
9/20 miles
So x+x^2=20
subtract 20 from both sdies
x^2+x-20=0
factor
find what 2 nmbers multiply to get -20 and add to get 1
factors of 20=2 times 2 times 5
the combos are
2 times 10
4 times 5
1 times 20
4 and 5 are 1 in diference
5-4=1
5 times 4=20
(x-4)(x+5)=0
if xy=0 then x and/or y=0
set each to zero
x-4=0
add 4
x=4
x+5=0
subtract 5
x=-5
but you want positive so this is an extranius answer so discard this
the number is 4