Solve for E
E=\frac{DE_{9}+5}{D^{2}}
D\neq 0
Solve for D (complex solution)
\left\{\begin{matrix}D=-\frac{\sqrt{20E+E_{9}^{2}}-E_{9}}{2E}\text{; }D=\frac{\sqrt{20E+E_{9}^{2}}+E_{9}}{2E}\text{, }&E\neq 0\\D=-\frac{5}{E_{9}}\text{, }&E=0\text{ and }E_{9}\neq 0\end{matrix}\right.
Solve for D
\left\{\begin{matrix}D=-\frac{\sqrt{20E+E_{9}^{2}}-E_{9}}{2E}\text{; }D=\frac{\sqrt{20E+E_{9}^{2}}+E_{9}}{2E}\text{, }&E\neq 0\text{ and }E\geq -\frac{E_{9}^{2}}{20}\\D=-\frac{5}{E_{9}}\text{, }&E=0\text{ and }E_{9}\neq 0\end{matrix}\right.
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DE_{9}+5=D^{2}E
Multiply D and D to get D^{2}.
D^{2}E=DE_{9}+5
Swap sides so that all variable terms are on the left hand side.
\frac{D^{2}E}{D^{2}}=\frac{DE_{9}+5}{D^{2}}
Divide both sides by D^{2}.
E=\frac{DE_{9}+5}{D^{2}}
Dividing by D^{2} undoes the multiplication by D^{2}.
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