For $5x^2+bx+4=0$, one root is 4/5. Find $b$.

Substituting $x=\frac{4}{5}:5\times \frac{16}{25}+\frac{4b}{5}+4=0$. Multiplying by 5 gives $16+4b+20=0$, so $b=-9$. Confirming with the formula on $5x^2-9x+4=0:D=81-80=1$ and $x=\frac{9\pm 1}{10}=1$ or $\frac{4}{5}$. Forgetting the minus sign when solving $4b=-36$ gives 9.