The area of a rectangle is 77ft^2 , and the length of the rectangle is 3ft more than twice the width. what are the dimensions of the rectangle ?

Area = 77 ft^2
W = W
L = 2W + 3

Area = L * W
Area = (2W + 3)*W
Area = 2W^2 + 3W
The area is also 77
So 
Area = 2w^2 + 3W = 77
Area = 2w^2 + 3W - 77 = 0
Now factor the question
77 can only factor into 1,77 which is highly unlikely and 7 and 11
As a guess I'm going to try 7. It that's true, we get
(x + 7)(2x - 11) = 0 This might work.
x^2 + 14x - 11x - 77 = 0
x^2 + 3x - 77 = 0 So the factoring is correct.

x + 7 = 0
x = - 7
2x - 11 = 0
2x = 11
x = 11/2
x = 5.5 
W = 5.5 <<<< Answer

The minus seven is meaningless.
Width = 5.5
Length = 2*5.5 + 3
Length = 11 + 3
Length = 14 <<<< answer

Now we have to check the area.
Area = L * W
Area = 14 * 5.5
Area = 77. You have a complete answer.