Let $ax^2 + bx +c = 0$ be a quadratic equation, then
Sum of roots $= \frac{-b}{a}$ and product of roots $= \frac{c}{a}$
$\color{red}{(6)_{ b} + (9)_{b} = (10)_{b} \Rightarrow b = 15}$
and $ (6)_{b}*(9)_{b} = (39)_{b}$ means $54 = 3b+ 9$, So $\color{blue}{b = 15}$