Solve 3a+p/2b=2b

$$3 a + \frac { p } { 2 b } = 2 b$$

Solve for a

$$a=\frac{2b}{3}-\frac{p}{6b}$$

$$b\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2b.

$$3a\times 2b+p=2b\times 2b$$

Multiply 3 and 2 to get 6.

$$6ab+p=2b\times 2b$$

Multiply b and b to get b^{2}.

$$6ab+p=2b^{2}\times 2$$

Multiply 2 and 2 to get 4.

$$6ab+p=4b^{2}$$

Subtract p from both sides.

$$6ab=4b^{2}-p$$

The equation is in standard form.

$$6ba=4b^{2}-p$$

Divide both sides by 6b.

$$\frac{6ba}{6b}=\frac{4b^{2}-p}{6b}$$

Dividing by 6b undoes the multiplication by 6b.

$$a=\frac{4b^{2}-p}{6b}$$

Divide 4b^{2}-p by 6b.

$$a=\frac{2b}{3}-\frac{p}{6b}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{\sqrt{4p+9a^{2}}+3a}{4}\text{, }&\left(|\frac{arg(a^{2})}{2}-arg(-a)|\geq \pi \text{ and }a\neq 0\right)\text{ or }p\neq 0\\b=\frac{-\sqrt{4p+9a^{2}}+3a}{4}\text{, }&\left(|\frac{arg(a^{2})}{2}-arg(a)|\geq \pi \text{ and }a\neq 0\right)\text{ or }p\neq 0\end{matrix}\right.$$

Solve for b

$$\left\{\begin{matrix}b=\frac{\sqrt{4p+9a^{2}}+3a}{4}\text{, }&\left(p\geq -\frac{9a^{2}}{4}\text{ and }a>0\text{ and }a\geq \frac{2\sqrt{-p}}{3}\text{ and }p\leq 0\right)\text{ or }p>0\text{ or }\left(|a|\geq \frac{2\sqrt{-p}}{3}\text{ and }p\geq -\frac{9a^{2}}{4}\text{ and }p<0\right)\\b=\frac{-\sqrt{4p+9a^{2}}+3a}{4}\text{, }&\left(p\geq -\frac{9a^{2}}{4}\text{ and }a<0\text{ and }a\leq -\frac{2\sqrt{-p}}{3}\text{ and }p\leq 0\right)\text{ or }p>0\text{ or }\left(|a|\geq \frac{2\sqrt{-p}}{3}\text{ and }p\geq -\frac{9a^{2}}{4}\text{ and }p<0\right)\end{matrix}\right.$$