Is it possible to solve this?

Shouldn't it be
y = ([sqrt(13)] - 7x)/-3
?

It should go:

Code:

(7x-3y)^2-6 = 7
(7x - 3y)^2 = 13
7x - 3y = sqrt(13)
-3y = sqrt(13) - 7x
y = ([sqrt(13)] - 7x)/-3

Since:

7x - 3y = -3y + 7x

Oh gawd now I'm scared of myself o.o

I'm also ashamed of Taiketo for not catching that mistake. Your syntax in the last line is wrong though.