SOLUTION: I am looking for the width of a golden rectangle where the length is given as 36inches. The formula I have been given is {{{L/W = W/(L-W)}}} where length divided by width is eq

Plug in 36 for the length L into




Cross-multiply:





Get 0 on the left, by adding -1296
and +36W to both sides:



Swap sides:



That doesn't factor, so we use the
quadratic formula:

 

 with



 









Write as the sum of two fractions:





Simplify the second term by dividing 18 and 2 by 2



That's OK like that or you may factor out
9:



Using the plus:

, approximately.

Using the minus:

, approximately.

We can discard the negative answer, since a rectangle
cannot have a negative side, and the width is given by:

 inches, approximately.

Edwin