Solve (2n-3)2n=5a

$$( 2 n - 3 ) 2 n = 5 a$$

Solve for a

$$a=\frac{2n\left(2n-3\right)}{5}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2n-3 by 2.

$$\left(4n-6\right)n=5a$$

Use the distributive property to multiply 4n-6 by n.

$$4n^{2}-6n=5a$$

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

$$5a=4n^{2}-6n$$

Divide both sides by 5.

$$\frac{5a}{5}=\frac{2n\left(2n-3\right)}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$a=\frac{2n\left(2n-3\right)}{5}$$

Solve for n (complex solution)

$$n=\frac{\sqrt{20a+9}+3}{4}$$

$$n=\frac{-\sqrt{20a+9}+3}{4}$$

Solve for n

$$n=\frac{\sqrt{20a+9}+3}{4}$$

$$n=\frac{-\sqrt{20a+9}+3}{4}\text{, }a\geq -\frac{9}{20}$$