Question

Linear equations-Transposition of formulae Why does this turn into this

Answer 1

That's not correct. In general, you would have

$x^2=\dfrac5{a^2}\implies\sqrt{x^2}=\sqrt{\dfrac5{a^2}}\implies |x|=\dfrac{\sqrt5}{\sqrt{a^2}}\implies |x|=\dfrac{\sqrt5}{|a|}$

Assuming $a>0$, you have $|a|=a$, so this turns into

$|x|=\dfrac{\sqrt5}a\implies x=\pm\dfrac{\sqrt5}a$