\(\dfrac{4}{16}=\dfrac{100}{x^2}-41\)
\(\Leftrightarrow\dfrac{4}{16}=\dfrac{100}{x^2}-\dfrac{41x^2}{x^2}\)
\(\Leftrightarrow\dfrac{4}{16}=\dfrac{100-41x^2}{x^2}\)
\(\Rightarrow4x^2=16\left(100-41x^2\right)\)
\(\Leftrightarrow4x^2=1600-656x^2\)
\(\Leftrightarrow1600-656x^2-4x^2=0\)
\(\Leftrightarrow-660x^2+1600=0\)
\(\Leftrightarrow-660x^2=-1600\)
\(\Leftrightarrow x^2=\dfrac{80}{33}\)
\(\Leftrightarrow x=\pm\dfrac{4\sqrt{165}}{33}\)
