Joint Poisson likelihood: $2\lambda^2-3\lambda-2=0$ gives $\hat\lambda=2$

Let X and Y be independent Poisson variables with $E(X)=\lambda$ and $E(Y)=\lambda+1$, when $\lambda>0$ is an unknown parameter. Based on single observations X and Y; $(X,Y)=(2,3)$, the MLE of $\lambda$ will be: