Let \(\alpha ,\beta\) be the roots of the quadratic equation \(12{x}^{2}−20x+3\lambda =0,\) \(\lambda \in Z.\) If \(\fra…

Let \(\alpha ,\beta\) be the roots of the quadratic equation \(12{x}^{2}−20x+3\lambda =0,\) \(\lambda \in Z.\) If \(\frac{1}{2}\leq \left|\beta −\alpha \right|\leq \frac{3}{2},\) then the sum of all possible values of \(\lambda\) is: