The area of a rectangle is 35 feet^2, and the length of the rectangle is 8 feet less than three times the width. find the dimensions of the rectangle

A = 35 ft^2 (square feet)
L=3W-8 (feet)
The formula for the area of this rect. is now A = W(3W-8) = 35 ft^2

3W^2 - 8W - 35 = 0
There are various ways in which we could solve this equation for W.
I have chosen to "factor by grouping."

3W^2 - 8W -35 = 0
3W^2 - 15W + 7W - 35 = 0
3W(W-5) + 7(W-5) = 0
Then (3W+7)(W-5)=0, and W=-7/3 or W=5.  Since W denotes width, and width cannot be negative, omit W=-7/3.  Thus, W=width=5 feet.
Next, L=3W-8=3(5)-8=15-8=7 feet.

Check:  Does (5 feet)(7 feet) come out to 35 square feet?  YES.

The dimensions of this rectangle are 5 by 7 feet.