Find the minimum of $f(x,y,z)=3x+2y+z+5$ subject to the constraint $g(x,y,z)=9x^2+4y-z=0$

Question

Let $ \displaystyle L(x,y,z,\lambda) =(3x+2y+z+5)+\lambda(9x^2+4y-z)$

By using Lagrange Multiplier

$L_x=3+18\lambda x=0$

$L_y=2+4\lambda=0$

$L_z=1-\lambda=0$

It implies that $\lambda=1=-2$?

How should I do next?