Let x represent the length of the picture. Then its width is represented by (x-13) and its area will be
A = length*width
30 = x(x -13)
This quadratic equation can be put into standard form and factored to find the solutions.
x² -13x -30 = 0
(x -15)(x +2) = 0
x ∈ {15, -2}
A negative length makes no sense, so we conclude ...
the length of the picture is 15 inches.