We have

12x^{2} - 20xy + 7y^{2} *≡(2x - y)(6x - 7y)*

Therefore, the sides of the triangle are

2x - y = 0 ......(1)

6x - 7y = 0 .....(2)

2x - 3y = -4 ......(3)

Solving Eqs. (1) and (2), we get (1,2) as the vertex. Solving Eqs. (2) and (3), we obtain (7, 6) as another vertex.By hypotheses, (0, 0) is the third vertex. Hence, the centroid of the triangle is

(0 + 1 + 7/3 , 0 + 2 + 6/3) = (8/3,8/3)