Question

What is X when 211 base X is equal to 152 base 8?

Answer 1

`211_x=2x^2+x+1`

`152_8=1\cdot8^2+5\cdot8+2=106_(10)`


`2x^2+x+1=106`

`2x^2+x-105=0`

`2\left(x+\frac{15}2\right)(x-7)=0`


`\implies x=-\frac{15}2\text{ or }x=7`

Presumably
`x` is a non-negative integer, which leaves
`x=7`, though it's not to say that rational solutions aren't necessarily excluded.