Solve 2a^2=2r+3/r

$$2 a ^ { 2 } = \frac { 2 r + 3 } { r }$$

Solve for r

$$r=\frac{3}{2\left(a^{2}-1\right)}$$

$$|a|\neq 1$$

Steps for Solving Linear Equation

Variable r cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by r.

$$2a^{2}r=2r+3$$

Subtract 2r from both sides.

$$2a^{2}r-2r=3$$

Combine all terms containing r.

$$\left(2a^{2}-2\right)r=3$$

Divide both sides by 2a^{2}-2.

$$\frac{\left(2a^{2}-2\right)r}{2a^{2}-2}=\frac{3}{2a^{2}-2}$$

Dividing by 2a^{2}-2 undoes the multiplication by 2a^{2}-2.

$$r=\frac{3}{2a^{2}-2}$$

Divide 3 by 2a^{2}-2.

$$r=\frac{3}{2\left(a^{2}-1\right)}$$

Variable r cannot be equal to 0.

$$r=\frac{3}{2\left(a^{2}-1\right)}\text{, }r\neq 0$$

Solve for a

$$a=\frac{\sqrt{4+\frac{6}{r}}}{2}$$

$$a=-\frac{\sqrt{4+\frac{6}{r}}}{2}\text{, }r\leq -\frac{3}{2}\text{ or }r>0$$