Let α, β be the roots of the quadratic equation 12 x^2-20 x+3 λ=0, λ ∈ Z. If 1/2 ≤|β-α| ≤ 3/2, then the sum of all possible values of λ is:

Let $\displaystyle \alpha, \beta$ be the roots of the quadratic equation $\displaystyle 12 x^2-20 x+3 \lambda=0, \lambda \in \mathbf{Z}$. If $\displaystyle \frac{1}{2} \leqslant|\beta-\alpha| \leqslant \frac{3}{2}$, then the sum of all possible values of $\displaystyle \lambda$ is :