In the traditional labelling of the quadratic, b is representd by 55 in the sought base. Since midway between the two solutions is 6.5, that must be the value of b/(2*5); that is, 55/5 = 11 must represent 13 in decimal so the base must be 12.
Does this check out? Assuming base 12, convert the equation to base 10:
5x^2  65x + 210 = 0
solutions:
65 +/ sqrt( 4225  4*1050)

10
= 6.5 +/ sqrt(25)/10
= 6.5 +/ 1/2
= 6 or 7
Base 12 checks out.

Posted by Charlie
on 20180701 10:08:08 