\(4y=\frac{3}{x^2}+2\) (1/equation)
\(\frac{1}{4y}=\frac{1}{\frac{3}{x^2}}+\frac{1}{2}\)
\(\frac{1}{4y}=\frac{x^2}{3}+\frac{1}{2}\) (*3)
\(\frac{3}{4y}=\frac{3x^2}{3}+\frac{3}{2}\)
\(\frac{3}{4y}=x^2+\frac{3}{2}\)
\(\frac{3}{4y}-\frac{3}{2}=x^2\)
\(x^2=\frac{3}{4y}-\frac{3}{2}\)
\(\sqrt{x^2}=\sqrt{\frac{3}{4y}-\frac{3}{2}}\)
\(|x|= \sqrt{\frac{3}{4y}-\frac{3}{2}}\)
\(x=\pm\sqrt{\frac{3}{4y}-\frac{3}{2}\)