What is the sum of all of the solutions of the equation $\frac{4x}{20}=\frac{5}{x}$?
To find the sum of all of the solutions, I need to first find all of the solutions. I can start by cross-multiplying to get rid of the fractions: $4x^2=100$. Then I can divide both sides by 4 to simplify: $x^2=25$. To get rid of the square, I need to take the square root of both sides, but remember that there are two possible roots: $x=\pm\sqrt{25}$. So the solutions are $x=5$ and $x=-5$. To find the sum, I just need to add them up: $5+(-5)=0$. 