Remove parentheses.
\[5x+4=3({x}^{-2}+7)\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[5x+4=3(\frac{1}{{x}^{2}}+7)\]
Expand.
\[5x+4=\frac{3}{{x}^{2}}+21\]
Multiply both sides by \({x}^{2}\).
\[5{x}^{3}+4{x}^{2}=3+21{x}^{2}\]
Move all terms to one side.
\[5{x}^{3}+4{x}^{2}-3-21{x}^{2}=0\]
Simplify \(5{x}^{3}+4{x}^{2}-3-21{x}^{2}\) to \(5{x}^{3}-17{x}^{2}-3\).
\[5{x}^{3}-17{x}^{2}-3=0\]
No root was found algebraically. However, the following root(s) were found by numerical methods.
\[x=3.450397\]
x=3.4503974914551
