The quadratic equation $(5a + 3k)x^2 + (2a-k)x+(a-2k)=0$, where a is a real constant and $k$ is a variable parameter, has the same roots for all real values of $k$. Find the two roots and the value of $a$.
My attempt: I have got the discriminant as $(-14a^2+25k^2+24ak)$, but could not proceed after that. Please help me to solve this question.