[Grade 12+ Maths: Lagrangian Optimization] Why can’t I solve this system of inequality like this?

I need a help because I don’t get why I can’t solve this inequality system like this, bc the value found is wrong.

We’re trying to find when the Lagrangian is equal to 0 with its constraint, and here we suppose that it’s constraint multiplier (lambda1) isn’t equal to 0.

This is in a context of finding critical points in an optimization with contraints of inequality.