Solve 2+2k^2=3ab^2

$$2 + 2 k ^ { 2 } = 3 a b ^ { 2 }$$

Solve for a

$$a=\frac{2\left(k^{2}+1\right)}{3b^{2}}$$

$$b\neq 0$$

Steps for Solving Linear Equation

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

$$3ab^{2}=2+2k^{2}$$

The equation is in standard form.

$$3b^{2}a=2k^{2}+2$$

Divide both sides by 3b^{2}.

$$\frac{3b^{2}a}{3b^{2}}=\frac{2k^{2}+2}{3b^{2}}$$

Dividing by 3b^{2} undoes the multiplication by 3b^{2}.

$$a=\frac{2k^{2}+2}{3b^{2}}$$

Divide 2+2k^{2} by 3b^{2}.

$$a=\frac{2\left(k^{2}+1\right)}{3b^{2}}$$

Solve for b

$$b=\frac{\sqrt{\frac{6\left(k^{2}+1\right)}{a}}}{3}$$

$$b=-\frac{\sqrt{\frac{6\left(k^{2}+1\right)}{a}}}{3}\text{, }a>0$$