6.267 x^{3}-\left(a^{2}-a+7\right) x-3\left(a^{2}-a-2\right)=0
$$
Solution. The given equation is a particular case of the model equation (1) if

we set $v=-3, u=\frac{3}{2}, w^{2}=\left(a-\frac{1}{2}\right)^{2}$.

Answer: $x_{1}=3, x_{2}=a+1, x_{3}=2-a$.