Solve m=n-ax^2/2

$$m = n- \frac{ a { x }^{ 2 } }{ 2 }$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{2\left(n-m\right)}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&m=n\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$n-\frac{ax^{2}}{2}=m$$

Subtract n from both sides.

$$-\frac{ax^{2}}{2}=m-n$$

Multiply both sides of the equation by 2.

$$-ax^{2}=2m-2n$$

Reorder the terms.

$$-ax^{2}=-2n+2m$$

The equation is in standard form.

$$\left(-x^{2}\right)a=2m-2n$$

Divide both sides by -x^{2}.

$$\frac{\left(-x^{2}\right)a}{-x^{2}}=\frac{2m-2n}{-x^{2}}$$

Dividing by -x^{2} undoes the multiplication by -x^{2}.

$$a=\frac{2m-2n}{-x^{2}}$$

Divide -2n+2m by -x^{2}.

$$a=-\frac{2\left(m-n\right)}{x^{2}}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{2\left(n-m\right)}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&m=n\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$n-\frac{ax^{2}}{2}=m$$

Subtract n from both sides.

$$-\frac{ax^{2}}{2}=m-n$$

Multiply both sides of the equation by 2.

$$-ax^{2}=2m-2n$$

Reorder the terms.

$$-ax^{2}=-2n+2m$$

The equation is in standard form.

$$\left(-x^{2}\right)a=2m-2n$$

Divide both sides by -x^{2}.

$$\frac{\left(-x^{2}\right)a}{-x^{2}}=\frac{2m-2n}{-x^{2}}$$

Dividing by -x^{2} undoes the multiplication by -x^{2}.

$$a=\frac{2m-2n}{-x^{2}}$$

Divide -2n+2m by -x^{2}.

$$a=-\frac{2\left(m-n\right)}{x^{2}}$$

Solve for m

$$m=-\frac{ax^{2}}{2}+n$$