Question 248126
The solutions {{{x=1/4}}} or {{{x=5}}} satisfy the equation {{{4x^2-21x+5=0}}}. However, we're not guaranteed that they satisfy the original equation {{{2x-5=sqrt(x+20)}}} (as extraneous roots may have been introduced).



To see if {{{x=1/4}}} is a solution to {{{2x-5=sqrt(x+20)}}}, simply plug it in to get: 


{{{2(1/4)-5=sqrt(1/4+20)}}}



{{{-9/2=sqrt(81/4)}}}



{{{-9/2=9/2}}} which is NOT true



So {{{x=1/4}}} is NOT a solution of {{{2x-5=sqrt(x+20)}}}



Similarly, plug in {{{x=5}}} into {{{2x-5=sqrt(x+20)}}} to get: 



{{{2(5)-5=sqrt(5+20)}}}



{{{5=sqrt(25)}}}



{{{5=5}}}



Since the equation is true, this verifies that {{{x=5}}} is a solution.



So the only solution is {{{x=5}}}