Solve for a
a=-\frac{2x-3}{x^{2}}
x\neq 0
Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{\sqrt{3a+1}-1}{a}\text{; }x=-\frac{\sqrt{3a+1}+1}{a}\text{, }&a\neq 0\\x=\frac{3}{2}\text{, }&a=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{\sqrt{3a+1}-1}{a}\text{; }x=-\frac{\sqrt{3a+1}+1}{a}\text{, }&a\neq 0\text{ and }a\geq -\frac{1}{3}\\x=\frac{3}{2}\text{, }&a=0\end{matrix}\right.
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ax^{2}-3=-2x
Subtract 2x from both sides. Anything subtracted from zero gives its negation.
ax^{2}=-2x+3
Add 3 to both sides.
x^{2}a=3-2x
The equation is in standard form.
\frac{x^{2}a}{x^{2}}=\frac{3-2x}{x^{2}}
Divide both sides by x^{2}.
a=\frac{3-2x}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
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