Question 80571
I guess that means you want values of a for which 

{{{ sqrt(9*a^2 + a - 7) = 3a }}}

The extraneous solutions that can occur are ones with {{{ a < 0 }}}
since the left side is always nonnegative.  (The question doesn't ask for solutions where + or - square root of 9a^2 + a - 7 is 3a.)

Square both sides

{{{ 9*a^2 + a - 7 = 9*a^2 }}}  and {{{ a>=0 }}}

Subtract 9*a^2 from both sides

{{{ a-7 = 0 }}} and {{{ a>= 0 }}}

{{{ a = 7 }}}

Check your answer:

{{{ sqrt(9*7^2 + 7 - 7) = 3*7 }}} ?

{{{ sqrt(441) = 21 }}} TRUE