Solve the equations for x and simplify the answer if possible. Indicate which solving technique is used, Linear, Factor, SRP ZPR, QF.1/6(3/4x-2)=(-1)/5

First six terms of the sequence $a_n=4-n$

${\displaystyle \alpha }$ and ${\displaystyle \beta }$ are the roots of the quadratic equation.
${\displaystyle \omega \ne 1}$ and ${\displaystyle {\omega }^{13}=1}$
If ${\displaystyle \alpha =\omega +{\omega }^3+{\omega }^4+{\omega }^{-4}+{\omega }^{-3}+{\omega }^{-1}}$
${\displaystyle \beta ={\omega }^2+{\omega }^5+{\omega }^6+{\omega }^{-6}+{\omega }^{-5}+{\omega }^{-2}}$,
then quadratic equation, whose roots are ${\displaystyle \alpha }$ and ${\displaystyle \beta }$ is:
I tried finding the sum and product of roots and placing in the equation $x^2-(\alpha +\beta )x+(\alpha \times \beta )=0$ but I was not able to solve for it.