Question 964193
{{{Sqrt(2x+5)=3+sqrt(x-2)}}}


Square BOTH sides.
{{{2x+5=(3+sqrt(x-2))^2}}}
{{{2x+5=9+6sqrt(x-2)+(x-2)}}}
Isolate the resulting radical.
{{{2x+5-9-(x-2)=6sqrt(x-2)}}}
{{{2x-4-x+2=6sqrt(x-2)}}}
{{{x-2=6sqrt(x-2)}}}
Square both sides again.
{{{x^2-4x+4=36(x-2)}}}
{{{x^2-4x+4=36x-72}}}
{{{x^2-4x-36x+4+72=0}}}
{{{x^2-40x+76=0}}}, which does not seem factorable.


{{{x=(40+- sqrt(40^2-4*76))/2}}}
{{{x=(40+- sqrt(1904))/2}}}


1904=16*119


{{{x=(40+- 4sqrt(119))/2}}}


{{{highlight(x=20+- 2sqrt(119))}}}


(Possible mistake in this work)