Answer
$-36$ and 15.
Work Step by Step
The sum of the solutions is$-12$.
Apply the formula to find the sum:
$\begin{align}
& -12=-\frac{-h}{3} \\
& -12=\frac{h}{3} \\
& h=-36
\end{align}$
Apply the formula to find the sum:
$\begin{align}
& 20=\frac{4k}{3} \\
& 20\left( 3 \right)=4k \\
& 60=4k
\end{align}$
Multiply by $\frac{1}{4}$ to get:
$\begin{align}
& \frac{60}{4}=\frac{4k}{4} \\
& 15=k
\end{align}$
Therefore, the values of h and k in the equation $3{{x}^{2}}-hx+4k=0$ are $-36$ and 15.
