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Let w = width
Let L = length
Length is 2 less than 7 times the width:
L = 7w - 2
Formula for area of a rectangle is A = w*L, and we know that A = 57
Substitute the formula for L into the equation, and solve for w:
57 = w(7w-2)
57 = 7w^2 - 2w
0 = 7w^2 - 2w -57
Use the quadratic equation (or WolframAlpha.com) to solve.
You should find that w=3
This means that L is:
So the dimensions are w=3, L=19.