The sum of all values of $x$ satisfying √$(2x+5)$ − √$(x-1)=2$ is:

Write √$(2x+5)=2$ + √$(x-1)$ and square: $2x+5=4+4$√$(x-1)+x-1$, so $x+2=4$√$(x-1)$. Squaring again gives $x^2+4x+4=16x-16$, i.e. $x^2-12x+20=0$, so $x=2$ or $x=10$. Both satisfy the original equation (√9 − √1 = 2 and √25 − √9 = 2), so the sum is 12.