Solve Vx+q/2x^2=H

$$Vx+ \frac{ q }{ 2 } { x }^{ 2 } = H$$

Solve for V (complex solution)

$$\left\{\begin{matrix}V=-\frac{qx}{2}+\frac{H}{x}\text{, }&x\neq 0\\V\in \mathrm{C}\text{, }&H=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Express \frac{q}{2}x^{2} as a single fraction.

$$Vx+\frac{qx^{2}}{2}=H$$

Subtract \frac{qx^{2}}{2} from both sides.

$$Vx=H-\frac{qx^{2}}{2}$$

Multiply both sides of the equation by 2.

$$2Vx=2H-qx^{2}$$

Reorder the terms.

$$2Vx=-qx^{2}+2H$$

The equation is in standard form.

$$2xV=2H-qx^{2}$$

Divide both sides by 2x.

$$\frac{2xV}{2x}=\frac{2H-qx^{2}}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$V=\frac{2H-qx^{2}}{2x}$$

Divide -qx^{2}+2H by 2x.

$$V=-\frac{qx}{2}+\frac{H}{x}$$

Solve for V

$$\left\{\begin{matrix}V=-\frac{qx}{2}+\frac{H}{x}\text{, }&x\neq 0\\V\in \mathrm{R}\text{, }&H=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Express \frac{q}{2}x^{2} as a single fraction.

$$Vx+\frac{qx^{2}}{2}=H$$

Subtract \frac{qx^{2}}{2} from both sides.

$$Vx=H-\frac{qx^{2}}{2}$$

Multiply both sides of the equation by 2.

$$2Vx=2H-qx^{2}$$

Reorder the terms.

$$2Vx=-qx^{2}+2H$$

The equation is in standard form.

$$2xV=2H-qx^{2}$$

Divide both sides by 2x.

$$\frac{2xV}{2x}=\frac{2H-qx^{2}}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$V=\frac{2H-qx^{2}}{2x}$$

Divide -qx^{2}+2H by 2x.

$$V=-\frac{qx}{2}+\frac{H}{x}$$

Solve for H

$$H=\frac{x\left(qx+2V\right)}{2}$$