Evaluation of base of a number in a quadratic expression....

The question is:
If the following quadratic expression is solved it results the decimal roots 8,5.what is the value of r?
x^2-(10)base r*x+(31)base r=0.

Here is the solution for the problem(according to me):
r is the base of the number 10 and 31.and if we evaluate the equation then we'll get root 8 and 5.
So, let r=8+5=13.
Now if we go with r=13,then we should get the value of x=8 & 5!
Now (10)base13=(13)base10 (converting into decimal)
and (31)base13=(40)base10 (converting into decimal)
=>x^2-(10)base r*x+(31)base r=0
=>x^2-13*x+40=0
=>x^2-8x-5x+40=0
=>x(x-8)-5(x-8)=0
=>(x-8)(x-5)=0
So,we get x=8,5.
So, r=13.