Find the max/min for $\displaystyle 3xy$ subject to $\displaystyle x^2 + y^2 = 8$

$\displaystyle L = 3xy - x^2\lambda - y^2\lambda + 8\lambda$

$\displaystyle L'(x) = 3y - 2x\lambda = 0$

$\displaystyle L'(y) = 3x -2y\lambda = 0$

$\displaystyle L'(\lambda) = -x^2 - y^2 + 8 = 0$

$\displaystyle 3y=2x\lambda$

$\displaystyle y=(2x\lambda)/3$

$\displaystyle 3x=3y\lambda$

$\displaystyle 3x=3((2x\lambda)/3)\lambda$

$\displaystyle x=4\lambda$

Am I doing anything wrong so far? I can't seem to get the right answer. All help appreciated!