Answer
$(4.78,218.67)$.
Work Step by Step
We set the two formulas equal and solve and solve for $x$.
$$
\begin{aligned}
2 x^3 & =100 \sqrt{x} \\
\frac{x^3}{x^{1 / 2}} & =\frac{100}{2} \\
x^{5 / 2} & =50 \\
x & =(50)^{2 / 5}=4.78176 .
\end{aligned}
$$
The corresponding $y$ value is
$$
y=100 \sqrt{4.78176}=218.672
$$
The coordinates of the point of intersection are $(4.78,218.67)$.
