Question 889512
Instead of writing several decimal expressions too early, assign variables to everything first, and solve completely in symbols.

Let A = area
Let w = width
Let L = length
Let k=0.6
L=k+2w, and A=4.6  both which come from the description.


{{{A=wL}}}
{{{A=w(k+2w)}}}
Remember, the only variable here now is w.  A and k are KNOWN.
{{{A=kw+2w^2}}}
{{{2w^2+kw=A}}}
{{{highlight_green(2w^2+kw-A=0)}}}


Not sure by looking at that which form of the general answer will be the acceptable one, but no matter---
{{{w=(-k+- sqrt(k^2-4*2*(-A)))/(4)}}}
The PLUS form will be wanted.
{{{highlight(w=(-k+sqrt(k^2+8A))/4)}}}


NOW plug in the assigned values of k and A and compute or evaluate w. Use this to evaluate L.
{{{w=(-0.6+sqrt(0.6^2+8*4.6))/4}}}
{{{w=(-0.6+sqrt(37.16))/4}}}
I'm getting about 1.37 for w.