It's impossible. The quadratic equation is ax^2 +b x +c =0, the coefficients are a, b, c. Integral coefficients are coefficients that are integers. - 2/3 and -1/5 aren't integers.

You will need to write the equation with some multiples of (x - 2/3) and (x + 1/5) to ensure that the function equals zero at each of the integral coefficients. An example would be (3x - 2) * (5x + 1) = 15x^2 - 7x - 2 = 0.