Solution. The given equation is a particular case of the model equation (1) if we set $v=1, u=\frac{1}{2}, w^{2}=\left(a-\frac{1}{2}\right)^{2}$.

Answer: $x_{1}=1, x_{2}=a, x_{3}=1-a$.
$6.258 x^{3}-2 x^{2}-\left(a^{2}-a-1\right) x+\left(a^{2}-a\right)=0$.

Translate the text above into English, keeping the original text's line breaks and format, and output the translation result directly.

$6.258 x^{3}-2 x^{2}-\left(a^{2}-a-1\right) x+\left(a^{2}-a\right)=0$.