Question 969826
(MISTAKE IS NOW FIXED.)


This kind of exercise is very common.


w, width
L, length
u, the uniform width to add around the garden.
A, <s>the amount of area increase.</s>---No.  That meaning is a mistake.   A is the new area of 208 square meters.
UNKNOWN is u.


Original area, {{{wL}}}.
New area, {{{(w+2u)(L+2u)=A}}}
Increase of area, {{{cross((w+2u)(L+2u)-wL=A)}}}.   <s>This is the equation to start 
working with.</s>



{{{cross(wL+2Lu+2wu+4u^2-wL=A)}}}
{{{(cross((2L+2w)u+4u^2-A=0)}}}
{{{cross(highlight(4u^2+(2L+2w)u-A=0))}}}


{{{wL+2uL+2uw+4u^2-A=0}}}
{{{highlight(4u^2+(2u+2L)u+wL-A=0)}}}------General-form quadratic equation in the variable(unknown), u.


You can solve the quadratic equation for u.  Substitute the values for L, w, and A any time you want.  You may want to substitute NOW, and simplify, before either factoring or do general solution, to finish.