Solve D=ax^2+7x

$$D = a x ^ { 2 } + 7 x$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{D-7x}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&D=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ax^{2}+7x=D$$

Subtract 7x from both sides.

$$ax^{2}=D-7x$$

The equation is in standard form.

$$x^{2}a=D-7x$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{D-7x}{x^{2}}$$

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

$$a=\frac{D-7x}{x^{2}}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{D-7x}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&D=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$ax^{2}+7x=D$$

Subtract 7x from both sides.

$$ax^{2}=D-7x$$

The equation is in standard form.

$$x^{2}a=D-7x$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{D-7x}{x^{2}}$$

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

$$a=\frac{D-7x}{x^{2}}$$

Solve for D

$$D=x\left(ax+7\right)$$