5x^2=100

To be precisely correct we need to include -2√5 as a solution, too.

5x^2=100

$$\begin{array}{rcl}
5\cdot x^2 &=& 100 \qquad| \quad :5 \\
x^2 &=& 20 \\
x^2 &=& 20 \qquad | \quad \sqrt\\
x &=& \sqrt {20} \\
x &=& \sqrt {4\cdot 5} \\
x &=& \sqrt {4} \cdot \sqrt {5} \qquad | \qaud \sqrt{4} = 2\\
x &=& 2 \cdot \sqrt {5} \\
\end{array}$$

That working out is perfectly fine!

Good spotting Chris :)