Solve 2n^2+5an-24=0

$$2 n ^ { 2 } + 5 a n - 24 = 0$$

Solve for a

$$a=-\frac{2n}{5}+\frac{24}{5n}$$

$$n\neq 0$$

Steps for Solving Linear Equation

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

$$5an-24=-2n^{2}$$

Add 24 to both sides.

$$5an=-2n^{2}+24$$

The equation is in standard form.

$$5na=24-2n^{2}$$

Divide both sides by 5n.

$$\frac{5na}{5n}=\frac{24-2n^{2}}{5n}$$

Dividing by 5n undoes the multiplication by 5n.

$$a=\frac{24-2n^{2}}{5n}$$

Divide -2n^{2}+24 by 5n.

$$a=-\frac{2n}{5}+\frac{24}{5n}$$

Solve for n

$$n=\frac{\sqrt{25a^{2}+192}-5a}{4}$$

$$n=\frac{-\sqrt{25a^{2}+192}-5a}{4}$$