Solve an^2+16n-26=0

$$a n ^ { 2 } + 16 n - 26 = 0$$

Solve for a

$$a=-\frac{2\left(8n-13\right)}{n^{2}}$$

$$n\neq 0$$

Steps for Solving Linear Equation

Subtract 16n from both sides. Anything subtracted from zero gives its negation.

$$an^{2}-26=-16n$$

Add 26 to both sides.

$$an^{2}=-16n+26$$

The equation is in standard form.

$$n^{2}a=26-16n$$

Divide both sides by n^{2}.

$$\frac{n^{2}a}{n^{2}}=\frac{26-16n}{n^{2}}$$

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

$$a=\frac{26-16n}{n^{2}}$$

Divide -16n+26 by n^{2}.

$$a=\frac{2\left(13-8n\right)}{n^{2}}$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=\frac{\sqrt{2\left(13a+32\right)}-8}{a}\text{; }n=-\frac{\sqrt{2\left(13a+32\right)}+8}{a}\text{, }&a\neq 0\\n=\frac{13}{8}\text{, }&a=0\end{matrix}\right.$$

Solve for n

$$\left\{\begin{matrix}n=\frac{\sqrt{2\left(13a+32\right)}-8}{a}\text{; }n=-\frac{\sqrt{2\left(13a+32\right)}+8}{a}\text{, }&a\neq 0\text{ and }a\geq -\frac{32}{13}\\n=\frac{13}{8}\text{, }&a=0\end{matrix}\right.$$