This is tricky
lets try substituting y = √)6x - 9)
√(6 - y) + √(6x + y) = √6
squaring both sides:-
6 - y + 6 + y - 2√(6 - y)(6 + y) = 6
12 - 2√(6 - y)(6 + y) = 6
√(6 - y)(6 + y) = (6-12) / -2 = 3
Squaring both sides:-
(6 - y)(6 + y) = 9
36 - y^2 = 9
y^2 = 27
y = +/-√27
√(6x - 9) = +/- 27
6x - 9 = 729
x = 738/6 = 123
This cannot be a solution because we would have a negative value for the
second square root
I would say that no solution exist.