Solve 12n^2-40x+32=0

$$12 n ^ { 2 } - 40 x + 32 = 0$$

Solve for x

$$x=\frac{3n^{2}}{10}+\frac{4}{5}$$

Steps for Solving Linear Equation

Subtract 12n^{2} from both sides. Anything subtracted from zero gives its negation.

$$-40x+32=-12n^{2}$$

Subtract 32 from both sides.

$$-40x=-12n^{2}-32$$

Divide both sides by -40.

$$\frac{-40x}{-40}=\frac{-12n^{2}-32}{-40}$$

Dividing by -40 undoes the multiplication by -40.

$$x=\frac{-12n^{2}-32}{-40}$$

Divide -12n^{2}-32 by -40.

$$x=\frac{3n^{2}}{10}+\frac{4}{5}$$

Solve for n (complex solution)

$$n=-\frac{\sqrt{30x-24}}{3}$$

$$n=\frac{\sqrt{30x-24}}{3}$$

Solve for n

$$n=\frac{\sqrt{30x-24}}{3}$$

$$n=-\frac{\sqrt{30x-24}}{3}\text{, }x\geq \frac{4}{5}$$