Show that the equation $\displaystyle x^2+(3a-2)x+a(a-1)=0$ has real roots for all values of a are real numbers ..

I tried this ..

$\displaystyle (3a-2)^2-4(a^2-a)$

$\displaystyle =9a^2-12a+4-4a^2+4a$

$\displaystyle =5a^2-8a+4$

Is it because $\displaystyle 5a^2-8a+4$ is a quadratic equation and hence it has real roots ? Or i am in the wrong path ...