Solve for a
a=\frac{6x+7}{x^{2}}
x\neq 0
Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{\sqrt{7a+9}+3}{a}\text{; }x=\frac{-\sqrt{7a+9}+3}{a}\text{, }&a\neq 0\\x=-\frac{7}{6}\text{, }&a=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{\sqrt{7a+9}+3}{a}\text{; }x=\frac{-\sqrt{7a+9}+3}{a}\text{, }&a\neq 0\text{ and }a\geq -\frac{9}{7}\\x=-\frac{7}{6}\text{, }&a=0\end{matrix}\right.
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ax^{2}+9=16+6x
Add 6x to both sides.
ax^{2}=16+6x-9
Subtract 9 from both sides.
ax^{2}=7+6x
Subtract 9 from 16 to get 7.
x^{2}a=6x+7
The equation is in standard form.
\frac{x^{2}a}{x^{2}}=\frac{6x+7}{x^{2}}
Divide both sides by x^{2}.
a=\frac{6x+7}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
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