I am given this equation of an unknown base:

It has a solution of x=5 and x=8 which are likely to be in our base 10.

I tried to find out the unknown base by comparing the co-efficients of the equations by doing so:

<--in base 10

<--in unknown base

Then I try to solve for the unknown base:

1*b = 13, b=13

but...

5*1 + 2*b = 40

2b = 35

b=17.5

How can the b in the equations be different? If this is the case, what is the actual base for the equation?

thanks!