Question 1050203
.
Of the two roots x = 7 and x = -10, only the root x = 7 satisfies the original equation.


The other root, x = -10, is extraneous and does not satisfies the original equation.


{{{graph( 330, 330, -3.5, 10.5, -3.5, 5.5,
          sqrt(2x+11)-sqrt(x+9), sqrt(x-6)
)}}}


Plots y = {{{sqrt(2x+11)-sqrt(x+9)}}} (red) and y = {{{sqrt(x-6)}}} (green)