Answer
Zero/s: $16$
$x$-intercept/s: $16$
Work Step by Step
To find the zeros of a function $f$, solve the equation $f(x)=0$
The zeros of the function are also the $x-$intercepts.
Let $g(x)=0$:
$$x+\sqrt{x}-20=0$$
Let $u=\sqrt{x}$, the original equation becomes
$$u^2+u-20=0$$
By factoring
$$(u+5)(u-4) = 0$$
Use the Zero-Product Property by equating each factor to zero, then solve each equation to obtain:
\begin{align*}
u +5&=0 &\text{ or }& &u-4=0\\
u &= -5 &\text{ or }& &u=4\\
\end{align*}
To solve for $x$, we use $u=\sqrt{x}$
For $u=-5$
$$\sqrt{x}=-5 \hspace{5pt} \to \hspace{5pt} \text{No Solution}$$
For $u=4$
$$\sqrt{x}=4$$
$$\therefore x = 16$$
$\therefore x =16$