Question 752809
{{{ a=4/(3-sqrt( 5 ))+4/a}}}


You ask for the value of a.

Multiply left side and right side by {{{ a*(3-sqrt(5))}}} .


{{{a*(3-sqrt(5))a=a(3-sqrt(5))(4/(3-sqrt( 5 ))+4/a)}}}
{{{a^2(3)-a^2*sqrt(5)=4a+4(3-sqrt(5))}}}
{{{3a^2-a^2*sqrt(5)=4a+12-4*sqrt(5)}}}
{{{3a^2-a^2*sqrt(5)-4a+4*sqrt(5)-12=0}}}
{{{highlight((3-sqrt(5))*a^2-4a+(4*sqrt(5)-12)=0)}}} which IS in the form of {{{mx^2+nx+p=0}}} and you can use the general solution for a quadratic eqaution.  You will certainly want to look for a good way to simplify the expression/s resulting.