The teacher will be very surprised to see your correct solution 😉
sqrt(18)-9*x = 3
sqrt18-9*x = 3
x = 3 / ((-9*x + 3*sqrt(2))/x)
___
1 \/ 2
x1 = - - + -----
3 3
x1 = -1/3 + sqrt(2)/3
sum
___ 1 \/ 2 - - + ----- 3 3
=
___ 1 \/ 2 - - + ----- 3 3
product
___ 1 \/ 2 - - + ----- 3 3
=
___ 1 \/ 2 - - + ----- 3 3
-1/3 + sqrt(2)/3