Solve q^2-na-144=0

$$q ^ { 2 } - n a - 144 = 0$$

Solve for a

$$\left\{\begin{matrix}a=\frac{q^{2}-144}{n}\text{, }&n\neq 0\\a\in \mathrm{R}\text{, }&n=0\text{ and }|q|=12\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$-na-144=-q^{2}$$

Add 144 to both sides.

$$-na=-q^{2}+144$$

The equation is in standard form.

$$\left(-n\right)a=144-q^{2}$$

Divide both sides by -n.

$$\frac{\left(-n\right)a}{-n}=\frac{144-q^{2}}{-n}$$

Dividing by -n undoes the multiplication by -n.

$$a=\frac{144-q^{2}}{-n}$$

Divide -q^{2}+144 by -n.

$$a=\frac{q^{2}-144}{n}$$

Solve for n

$$\left\{\begin{matrix}n=\frac{q^{2}-144}{a}\text{, }&a\neq 0\\n\in \mathrm{R}\text{, }&a=0\text{ and }|q|=12\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$-na-144=-q^{2}$$

Add 144 to both sides.

$$-na=-q^{2}+144$$

The equation is in standard form.

$$\left(-a\right)n=144-q^{2}$$

Divide both sides by -a.

$$\frac{\left(-a\right)n}{-a}=\frac{144-q^{2}}{-a}$$

Dividing by -a undoes the multiplication by -a.

$$n=\frac{144-q^{2}}{-a}$$

Divide -q^{2}+144 by -a.

$$n=\frac{q^{2}-144}{a}$$