Question 872550
Requires squaring both sides twice, but not all at once.


{{{2sqrt(5m^2)+3m=4sqrt(5)}}}
{{{4*5m^2+2*2*3*m*sqrt(5m^2)+9m^2=16*5}}}
{{{20m^2+12m*sqrt(5m^2)=-9m^2+80}}}
{{{12m*sqrt(5m^2)=-20m^2-9m^2+80}}}
{{{12m*sqrt(5m^2)=80-29m^2}}}
Another Squaring...
{{{144m^2*5m^2=6400-2*80*29m^2+29^2*m^4}}}
{{{720m^4=6400-4640m^2+841m^4}}}
{{{highlight_green(121m^4-4640m^2+6400=0)}}}-----This is in quadratic form, so first solve for m^2 and then continue on to m.  .


Discriminant?  {{{4640^2-4*121*6400=21529600-3097600=18432000}}}
{{{1000*9*2048=512*4*9*1000=128*4*4*9*1000=32*4*4*4*9*1000=4*8(4*4*4)*9*1000=
2*4^5*9*100*2*5=4^6*5*9*2*100}}}
{{{sqrt(D)=3*4^3*10sqrt(10)=1920sqrt(10)}}}


Quadratic Formula Solution gives:
{{{highlight(m^2=(4640+- 1920sqrt(10))/(2*121))}}}
This is still unfinished, needing the two solutions for m, from this one for m^2.