Question 890221
w for width and L for length:
-4+w=-23+2L from the second sentence description.  
That gives {{{w-2L=4-23}}},
{{{w-2L=-19}}}
{{{2L-w=19}}}.


Area description means {{{wL=10}}}.
Choose either w or L and substitute for it in the area equation.  Maybe w is most convenient to use.  w=2L-19.
{{{highlight((2L-19)L=10)}}}, when substituted.


Standard form for the equation is not really the best way to go.  Just try simplifying, and if possible, factoring.


{{{highlight(2L^2-19L-10=0)}}}, general form.
Discriminant?  19^2-4*2(-10)=19^2+80=441=21^2.
Directly using general solution of a quadratic equation and the values from the equation,
{{{L=(19+- 21)/4}}}  MUST be only {{{highlight(L=(19+21)/4=10)}}}.


Use this in formula for w to find w.