Solve -un^2+5un+6=0

$$- u n ^ { 2 } + 5 u n + 6 = 0$$

Solve for u

$$u=-\frac{6}{n\left(5-n\right)}$$

$$n\neq 5\text{ and }n\neq 0$$

Steps for Solving Linear Equation

Subtract 6 from both sides. Anything subtracted from zero gives its negation.

$$\left(-u\right)n^{2}+5un=-6$$

Reorder the terms.

$$5nu-un^{2}=-6$$

Combine all terms containing u.

$$\left(5n-n^{2}\right)u=-6$$

Divide both sides by -n^{2}+5n.

$$\frac{\left(5n-n^{2}\right)u}{5n-n^{2}}=-\frac{6}{5n-n^{2}}$$

Dividing by -n^{2}+5n undoes the multiplication by -n^{2}+5n.

$$u=-\frac{6}{5n-n^{2}}$$

Divide -6 by -n^{2}+5n.

$$u=-\frac{6}{n\left(5-n\right)}$$

Solve for n (complex solution)

$$n=-\frac{\sqrt{u\left(25u+24\right)}-5u}{2u}$$

$$n=\frac{\sqrt{u\left(25u+24\right)}+5u}{2u}\text{, }u\neq 0$$

Solve for n

$$n=-\frac{\sqrt{u\left(25u+24\right)}-5u}{2u}$$

$$n=\frac{\sqrt{u\left(25u+24\right)}+5u}{2u}\text{, }u>0\text{ or }u\leq -\frac{24}{25}$$