Question 249634
L=2w +1
this is good
2w^2+w-78=0
divide by 2
w^2+w/2-39=0
w^2+w/2=39

[how did you get (2w + 13) and (2w - 6)
I see the 78 but where is the w?
I get 26w-12w=14w not 1w
to factor you need factors of 78 with a difference of one.
78,1
39,2
13,6
26,3
prime factors
13,3,2,1
there aren't any whole numbers]

complete the square
((1/2)(/2))^2
(1/4)^2=1/16
add 1/16 to both sides

w^2+w/2+1/16=39
(w+1/4)^2=625/16
w+1/4=+\-25/4

w=-1/4+25/4=24/4=6
w=-1/4-25/4=-26/4=-13/2
we can't use the negative solution so we have 6 for w
l=2w+1
l=13

*[invoke quadratic "x", 2, 1, -78]
*[invoke quadratic "x", 1, 1/2, -39 ]