Solve sqrt{2}a=a+2/3b

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

Solve for a

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

Steps for Solving Linear Equation

Subtract a from both sides.

$$\sqrt{2}a-a=\frac{2}{3}b$$

Combine all terms containing a.

$$\left(\sqrt{2}-1\right)a=\frac{2}{3}b$$

The equation is in standard form.

$$\left(\sqrt{2}-1\right)a=\frac{2b}{3}$$

Divide both sides by \sqrt{2}-1.

$$\frac{\left(\sqrt{2}-1\right)a}{\sqrt{2}-1}=\frac{2b}{3\left(\sqrt{2}-1\right)}$$

Dividing by \sqrt{2}-1 undoes the multiplication by \sqrt{2}-1.

$$a=\frac{2b}{3\left(\sqrt{2}-1\right)}$$

Divide \frac{2b}{3} by \sqrt{2}-1.

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

Solve for b

$$b=\frac{3\left(\sqrt{2}-1\right)a}{2}$$

Steps for Solving Linear Equation

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

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

Subtract a from both sides.

$$\frac{2}{3}b=\sqrt{2}a-a$$

Divide both sides of the equation by \frac{2}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{2}{3}b}{\frac{2}{3}}=\frac{\left(\sqrt{2}-1\right)a}{\frac{2}{3}}$$

Dividing by \frac{2}{3} undoes the multiplication by \frac{2}{3}.

$$b=\frac{\left(\sqrt{2}-1\right)a}{\frac{2}{3}}$$

Divide a\left(\sqrt{2}-1\right) by \frac{2}{3} by multiplying a\left(\sqrt{2}-1\right) by the reciprocal of \frac{2}{3}.

$$b=\frac{3\left(\sqrt{2}-1\right)a}{2}$$