Question 936217
You should draw a picture of the description.
Assign some variables:
w, width of the parking lot
L, length of the parking lot
u, the uniform width of sidewalk
T, total area of parking lot and sidewalk;
L=w+15, and if wanted, a variable could be assigned for "15".
Unknown variables are w and L.


You are also given:
u=4;
T=46384.



Setup some expressions and equations.
Lot area,  wL, or {{{w(w+15)}}}.
'
{{{T=(w+2u)(L+2u)}}}
{{{T=(w+2u)(w+15+2u)}}}
{{{highlight(T=w^2+(4u+15)w+30u+4u^2)}}}



Check the composition of that equation carefully.  The ONLY unknown is w, and this, parking lot width, is what the question is to be answered.  All the other variables are KNOWN.   You have a choice of solving for w completely symbolically, or substituting the known values now and simplifying, and then solving for w.  Substituting for u and T now and simplifying would probably be more comfortable.


....otherwise, you can go ahead with
{{{w=(-4u-15+- sqrt((4u+15)^2-4*1*(4u^2+30u-T)))/2}}}
and try to simplify it....