Solve Delta_{n}=2+sqrt{2}n

$$\Delta _ { n } = 2 + \sqrt { 2 } n$$

Solve for n

$$n=-\frac{\sqrt{2}\left(2-\Delta _{n}\right)}{2}$$

Steps for Solving Linear Equation

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

$$2+\sqrt{2}n=\Delta _{n}$$

Subtract 2 from both sides.

$$\sqrt{2}n=\Delta _{n}-2$$

Divide both sides by \sqrt{2}.

$$\frac{\sqrt{2}n}{\sqrt{2}}=\frac{\Delta _{n}-2}{\sqrt{2}}$$

Dividing by \sqrt{2} undoes the multiplication by \sqrt{2}.

$$n=\frac{\Delta _{n}-2}{\sqrt{2}}$$

Divide \Delta _{n}-2 by \sqrt{2}.

$$n=\frac{\sqrt{2}\left(\Delta _{n}-2\right)}{2}$$

Solve for Δ_n

$$\Delta _{n}=\sqrt{2}n+2$$