$$G=(5b-2)(-3b+2)$$
$G=\left(2-5b\right)\left(3b-2\right)$
$b=\frac{\sqrt{4-15G}+8}{15}$
$b=\frac{-\sqrt{4-15G}+8}{15}\text{, }G\leq \frac{4}{15}$
