Solve kn^2/2=n/6+1/3

$$k \frac { n ^ { 2 } } { 2 } = \frac { n } { 6 } + \frac { 1 } { 3 }$$

Solve for k

$$k=\frac{n+2}{3n^{2}}$$

$$n\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,6,3.

$$3kn^{2}=n+2$$

The equation is in standard form.

$$3n^{2}k=n+2$$

Divide both sides by 3n^{2}.

$$\frac{3n^{2}k}{3n^{2}}=\frac{n+2}{3n^{2}}$$

Dividing by 3n^{2} undoes the multiplication by 3n^{2}.

$$k=\frac{n+2}{3n^{2}}$$

Solve for n

$$\left\{\begin{matrix}n=\frac{\sqrt{24k+1}+1}{6k}\text{; }n=\frac{-\sqrt{24k+1}+1}{6k}\text{, }&k\neq 0\text{ and }k\geq -\frac{1}{24}\\n=-2\text{, }&k=0\end{matrix}\right.$$