In what base does the equation $x^2 - 11x + 22 = 0$ have solutions $6$ and $3$? If we have below equation and know that $6$ and $3$ are answers of this equation, how to obtain the base used in the equation?
$$x^2 - 11x + 22 = 0$$
Partial result
The base is not $10$. (Because  $3^2-3\cdot 11+22\ne 0$ in base $10$.)

Knowing the roots you have
$$(x-3)(x-6) = x^2 -9x + 18$$
and therefore the base is 8. Check:  $9=11_8$ and $18=22_8$.
