From the image, and using the Pythagorean theorem in ΔABC:
[tex]\begin{gathered} AB^2+AC^2=BC^2 \\ 15^2+AC^2=20^2 \\ 225+AC^2=400 \\ AC^2=175 \\ AC=5\sqrt{7} \end{gathered}[/tex]
Additionally, we know that:
[tex]\begin{gathered} CD+DB=BC \\ \Rightarrow DB=20-x \end{gathered}[/tex]
Finally, using the altitude on hypotenuse theorem:
[tex]\begin{gathered} AC^2=CD\cdot BC \\ 15^2=x\cdot20 \\ \therefore x=\frac{45}{4} \end{gathered}[/tex]
