[tex]211_x=2x^2+x+1[/tex]
[tex]152_8=1\cdot8^2+5\cdot8+2=106_{10}[/tex]
[tex]2x^2+x+1=106[/tex]
[tex]2x^2+x-105=0[/tex]
[tex]2\left(x+\dfrac{15}2\right)(x-7)=0[/tex]
[tex]\implies x=-\dfrac{15}2\text{ or }x=7[/tex]
Presumably [tex]x[/tex] is a non-negative integer, which leaves [tex]x=7[/tex], though it's not to say that rational solutions aren't necessarily excluded.
