[tex]\displaystyle\\
a)\\
24:x=4 \sqrt{3} \\\\
\frac{24}{x} =4\sqrt{3} \\\\
x=\frac{24}{4\sqrt{3}}= \frac{6}{\sqrt{3}}=\frac{6\sqrt{3}}{3}=\boxed{\bf 2\sqrt{3}}\\\\
b)\\
20:x=2 \sqrt{5}\\\\
\frac{20}{x} =2\sqrt{5}\\\\
x=\frac{20}{2\sqrt{5}}=\frac{10}{\sqrt{5}}=\frac{10\sqrt{5}}{5}=\boxed{\bf 2\sqrt{5}}\\\\
c)\\
45:x=5\sqrt{3}\\\\
\frac{45}{x}=5\sqrt{3}\\\\
x=\frac{45}{5\sqrt{3}}=\frac{9}{\sqrt{3}}=\frac{9\sqrt{3}}{3}=\boxed{\bf3\sqrt{3}}[/tex]
[tex]\displaystyle
d)\\
(-7\sqrt{10}):x=7\sqrt{2}\\\\
\frac{-7\sqrt{10}}{x}= 7\sqrt{2}\\\\
x=\frac{-7\sqrt{10}}{7\sqrt{2}}=\boxed{\bf -\sqrt{5}}[/tex]