Lagrange multiplier expression

Question

I would like to solve the following optimization problem using the gradient ascend method: \begin{array}{ll} \text{maximize}_{\theta} & \theta^TQ_1\theta + b_1\\ \text{subject to} & \theta^TQ_2\theta+ b_2 \leq \alpha \end{array} So I would like to find the langrage multiplier $\lambda$ such that my problem becomes ${\arg\max}_{\theta}~\theta^TQ_1\theta+b_1-\lambda\big(\theta^TQ_2\theta+b_2\big)$ where $\lambda$, $b_1,b_2$ are scalars, $\theta\in\mathbb{R}^{2\times1}$, $Q_1\in\mathbb{R}^{2\times2}$ is negative definite and $Q_2\in\mathbb{R}^{2\times2}$ is positive definite. I expect the expression of $\lambda $ to be in terms of $\alpha$ to not violate the constraint $\theta^TQ_2\theta+b_2\leq \alpha$.