Given a utility function $R(x,y) = x(100-6x) + y(192-4y)$ and a constraint equation $C(x,y) = 2x^2+2y^2+4xy-8x=-20$, maximize.
As usual with Lagrange, I got stuck on the juicier part of solving a set of equations: Lagrangian function $L = x(100-6x) + y(192-4y) - \lambda(2x^2+2y^2+4xy-8x+20)$
$$L_x = 100−12x-λ(4x+4y−8)$$
$$L_y = 192-8y-4\lambda(x+y)$$
setting $L_x$ and $L_y$ to 0, I get $12x+\lambda(4x+4y-8)$ = 100 and $8y-4\lambda(x+y) = 192$
And here's where I got stuck. Anyone have any ideas?