Answer
Real zero $25$
x-intercept $25$.
Work Step by Step
Step 1. Real zeros, treat $\sqrt x$ as a single unit, $3x-13\sqrt x-10=0 \longrightarrow 3(\sqrt x)^2-13(\sqrt x)-10=0 \longrightarrow (3\sqrt x+2)(\sqrt x-5)=0 \longrightarrow x=25$
Step 2. The x-intercept is the same as the real zeros, that is $ x=25$.