Question

Determine the value of base x if (211)x = (6A)16

Answer 1

$211_x=2x^2+x+1$
$6A_{16}=106_{10}$

$\implies 2x^2+x+1=106\iff 2x^2+x-105=(x-7)(2x+15)=0$

This has two solutions, $x=7$ and $x=-\dfrac{15}2$.