Question 764333
Let w = width of the frame.


Total area of the frame and picture = {{{(7+2w)(8+2w)=182}}} which will obviously be quadratic.  
Begin to simplify.
{{{56+16w+14w+4w^2=182}}}
{{{4w^2+30w+56=182}}}
{{{4w^2+30w-126=0}}}
{{{2w^2+15w-63=0}}}


Use general solution unless you see a way to factor if possible.