Solve h^2=q(h-1)/2

$$h ^ { 2 } = \frac { q ( h - 1 ) } { 2 }$$

Solve for q

$$q=-\frac{2h^{2}}{1-h}$$

$$h\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2h^{2}=q\left(h-1\right)$$

Use the distributive property to multiply q by h-1.

$$2h^{2}=qh-q$$

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

$$qh-q=2h^{2}$$

Combine all terms containing q.

$$\left(h-1\right)q=2h^{2}$$

Divide both sides by h-1.

$$\frac{\left(h-1\right)q}{h-1}=\frac{2h^{2}}{h-1}$$

Dividing by h-1 undoes the multiplication by h-1.

$$q=\frac{2h^{2}}{h-1}$$

Solve for h

$$h=\frac{\sqrt{q\left(q-8\right)}+q}{4}$$

$$h=\frac{-\sqrt{q\left(q-8\right)}+q}{4}\text{, }q\geq 8\text{ or }q\leq 0$$