Find the maxima and the minima of the given function given the constraint.

Constraint:

Using the Lagrange Multiplier method, I managed to obtain

Solving for the variables gave me:

So then I plug these values into my constraint to end up with

Then I end up with the quadratic, after simplifying;

However, this quadratic can't be solved using real numbers. Have I done anything wrong or am I using the wrong approach?

Thank you