solving a word problem using a quadratic equation with rational roots

Question

The area of a rectangle is 54 ft^2, and the length of the rectangle is 3 ft more than twice the width. Find the dimensions of the rectangle. 

Answer-

Length: ____ ft

Width: ___ ft

Thanks in advance! :D 

Answer 1

Let w = the width

Let 2w + 3 = the length

A = lw

54 = w(2w+3)

54 = 2w² + 3w

2w² + 3w - 54 = 0

(2w-9)(w+6) = 0

2w - 9 = 0      or    w + 6 = 0
2w = 9           or           w = -6, illogical answer

w = 4 1/2 feet

Length = 2w + 3 = 2(9/2) + 3 = 9 + 3

length = 12 feet