The equations $$3x^{2}-5x+p=0$$ and $$2x^{2}-2x+q=0$$ have one common root. The sum of the other roots of this equations is

Let's assume that the common root is r. 

The sum of the roots of the first equation is 5/3 and that of the second equation is 1.

We want the sum of the other two roots:

$$ \text{Sum} = \left(\frac{5}{3}-r\right) + (1-r) = \frac{8}{3}-2r$$

We now need to express r in terms of p and q.

Since r is a common root, it satisfies:

$$3r^2 - 5r + p = 0 \quad (1)$$

$$ 2r^2 - 2r + q = 0 \quad (2)$$

Eliminate $$ r^2$$ .

Multiply (2) by 3:

$$ 6r^2 - 6r + 3q = 0$$

Multiply (1) by 2:

$$ 6r^2 - 10r + 2p = 0$$

Subtract:

$$ (6r^2 - 6r + 3q) - (6r^2 - 10r + 2p) = 0$$

$$ 4r + 3q - 2p = 0$$

$$  r = \frac{2p - 3q}{4}$$

Now substitute into $$ \frac{8}{3} - 2r$$ :

$$ \frac{8}{3} - 2\left(\frac{2p - 3q}{4}\right)$$

$$ = \frac{8}{3} - \frac{2p - 3q}{2}$$

$$ = \frac{8}{3} - p + \frac{3}{2}q$$