Solve ax^2+Bx-C=0

$$a x ^ { 2 } + B x - C = 0$$

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. Anything subtracted from zero gives its negation.

$$Bx-C=-ax^{2}$$

Add C to both sides.

$$Bx=-ax^{2}+C$$

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 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. Anything subtracted from zero gives its negation.

$$Bx-C=-ax^{2}$$

Add C to both sides.

$$Bx=-ax^{2}+C$$

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 C

$$C=x\left(ax+B\right)$$

Steps for Solving Linear Equation

Subtract ax^{2} from both sides. Anything subtracted from zero gives its negation.

$$Bx-C=-ax^{2}$$

Subtract Bx from both sides.

$$-C=-ax^{2}-Bx$$

Divide both sides by -1.

$$\frac{-C}{-1}=-\frac{x\left(ax+B\right)}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$C=-\frac{x\left(ax+B\right)}{-1}$$

Divide -x\left(ax+B\right) by -1.

$$C=x\left(ax+B\right)$$