Question 892645
{{{w=-5+2L}}} and {{{wL=72}}}.


{{{(2L-5)L=72}}}
{{{2L^2-5L-72=0}}}


{{{L=(5+- sqrt(25+4*2*72))/4}}}
{{{L=(5+- sqrt(1800))/4}}}
{{{L=(5+- 10sqrt(2*3*3))/4}}}
{{{L=(5+- 30sqrt(2))/4}}}, choose the PLUS form.
{{{highlight(L=(5+30sqrt(2))/4)}}}


Just use the earlier described formula for w to find its value from L.
You can use either initially described formulas, including wL=72 if you want.
{{{w=72/L}}}.  If do that,
{{{w=72/((5+30sqrt(2))/4)}}}
{{{w=(72*4)/(5+30sqrt(2))}}}, and should rationalize the denominator.
{{{w=(72*4(5-30sqrt(2)))/(25-900*2)}}}
{{{w=(72*4(30sqrt(2)-5))/(1800-25)}}}
{{{w=(72*4*5(6sqrt(2)-1))/1775}}}
{{{w=(72*4(6sqrt(2)-1))/355}}}
{{{highlight(w=(288/355)(6sqrt(2)-1))}}}----maybe the linear form would have been easier.  Should have used {{{2L-5}}} instead.