Solve 0=a^2-969n+410

$$0 = a ^ { 2 } - 969 n + 410$$

Solve for n

$$n=\frac{a^{2}+410}{969}$$

Steps for Solving Linear Equation

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

$$a^{2}-969n+410=0$$

Subtract a^{2} from both sides. Anything subtracted from zero gives its negation.

$$-969n+410=-a^{2}$$

Subtract 410 from both sides.

$$-969n=-a^{2}-410$$

Divide both sides by -969.

$$\frac{-969n}{-969}=\frac{-a^{2}-410}{-969}$$

Dividing by -969 undoes the multiplication by -969.

$$n=\frac{-a^{2}-410}{-969}$$

Divide -a^{2}-410 by -969.

$$n=\frac{a^{2}+410}{969}$$

Solve for a

$$a=\sqrt{969n-410}$$

$$a=-\sqrt{969n-410}\text{, }n\geq \frac{410}{969}$$