Solve AX^2+BX=C

$$A X ^ { 2 } + B X = C$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=-\frac{BX-C}{X^{2}}\text{, }&X\neq 0\\A\in \mathrm{C}\text{, }&C=0\text{ and }X=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract BX from both sides.

$$AX^{2}=C-BX$$

The equation is in standard form.

$$X^{2}A=C-BX$$

Divide both sides by X^{2}.

$$\frac{X^{2}A}{X^{2}}=\frac{C-BX}{X^{2}}$$

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

$$A=\frac{C-BX}{X^{2}}$$

Solve for B (complex solution)

$$\left\{\begin{matrix}B=-AX+\frac{C}{X}\text{, }&X\neq 0\\B\in \mathrm{C}\text{, }&C=0\text{ and }X=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract AX^{2} from both sides.

$$BX=C-AX^{2}$$

Reorder the terms.

$$BX=-AX^{2}+C$$

The equation is in standard form.

$$XB=C-AX^{2}$$

Divide both sides by X.

$$\frac{XB}{X}=\frac{C-AX^{2}}{X}$$

Dividing by X undoes the multiplication by X.

$$B=\frac{C-AX^{2}}{X}$$

Divide C-AX^{2} by X.

$$B=-AX+\frac{C}{X}$$

Solve for A

$$\left\{\begin{matrix}A=-\frac{BX-C}{X^{2}}\text{, }&X\neq 0\\A\in \mathrm{R}\text{, }&C=0\text{ and }X=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract BX from both sides.

$$AX^{2}=C-BX$$

The equation is in standard form.

$$X^{2}A=C-BX$$

Divide both sides by X^{2}.

$$\frac{X^{2}A}{X^{2}}=\frac{C-BX}{X^{2}}$$

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

$$A=\frac{C-BX}{X^{2}}$$

Solve for B

$$\left\{\begin{matrix}B=-AX+\frac{C}{X}\text{, }&X\neq 0\\B\in \mathrm{R}\text{, }&C=0\text{ and }X=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract AX^{2} from both sides.

$$BX=C-AX^{2}$$

Reorder the terms.

$$BX=-AX^{2}+C$$

The equation is in standard form.

$$XB=C-AX^{2}$$

Divide both sides by X.

$$\frac{XB}{X}=\frac{C-AX^{2}}{X}$$

Dividing by X undoes the multiplication by X.

$$B=\frac{C-AX^{2}}{X}$$

Divide C-AX^{2} by X.

$$B=-AX+\frac{C}{X}$$