Solve for a (complex solution)
\left\{\begin{matrix}a=-\frac{b-3}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&b=3\text{ and }x=0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=-\frac{b-3}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&b=3\text{ and }x=0\end{matrix}\right.
Solve for b
b=3-ax^{2}
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ax^{2}+b=3
Swap sides so that all variable terms are on the left hand side.
ax^{2}=3-b
Subtract b from both sides.
x^{2}a=3-b
The equation is in standard form.
\frac{x^{2}a}{x^{2}}=\frac{3-b}{x^{2}}
Divide both sides by x^{2}.
a=\frac{3-b}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
ax^{2}+b=3
Swap sides so that all variable terms are on the left hand side.
ax^{2}=3-b
Subtract b from both sides.
x^{2}a=3-b
The equation is in standard form.
\frac{x^{2}a}{x^{2}}=\frac{3-b}{x^{2}}
Divide both sides by x^{2}.
a=\frac{3-b}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
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