The roots of the quadratic equation \(2x^2+kx+3=0\), where \(k>0\), are \(\alpha\) and \(\beta\), whilst those of the equation \(3x^2-2x+3\) are \(\dfrac{\alpha}{\beta}\) and \(\dfrac{\beta}{\alpha}\). Calculate the value of \(k\).

The roots of the quadratic equation \(2x^2+kx+3=0\), where \(k>0\), are \(\alpha\) and \(\beta\), whilst those of the equation \(3x^2-2x+3\) are \(\dfrac{\alpha}{\beta}\) and \(\dfrac{\beta}{\alpha}\). Calculate the value of \(k\).