Question 49645
  
  Hello,
         You have done correctly till the third line from the last. So your answer has gone wrong. From the second line from the last I have done it here. Please check up.

{{{(12+-sqrt(128))/(-4))}}} = {{{(12 +- 8sqrt(2))/(-4))}}}
Now let us take {{{(12 + 8sqrt(2))/(-4))}}}
 
{{{(12 + 8sqrt(2))/(-4))}}} = {{{-3+(-2)sqrt(2)}}} = {{{-3-2sqrt(2)}}}  ...   ...  (1)
 
Now let us take {{{(12 - 8sqrt(2))/(-4))}}}
 
{{{(12 - 8sqrt(2))/(-4))}}} = {{{-3-(-2)sqrt(2)}}} = {{{-3+2sqrt(2)}}}  .....  ....  (2)

From the (1) and (2) above, we can make out 

Solution set = ({{{-3 -2sqrt(2)}}}, {{{-3+2sqrt(2)}}})  Answer.
I hope this is clear to you.