Solve y^2=2/3(x-1)

$$y ^ { 2 } = \frac { 2 } { 3 } ( x - 1 )$$

Solve for x

$$x=\frac{3y^{2}}{2}+1$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by x-1.

$$y^{2}=\frac{2}{3}x-\frac{2}{3}$$

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

$$\frac{2}{3}x-\frac{2}{3}=y^{2}$$

Add \frac{2}{3} to both sides.

$$\frac{2}{3}x=y^{2}+\frac{2}{3}$$

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

$$\frac{\frac{2}{3}x}{\frac{2}{3}}=\frac{y^{2}+\frac{2}{3}}{\frac{2}{3}}$$

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

$$x=\frac{y^{2}+\frac{2}{3}}{\frac{2}{3}}$$

Divide y^{2}+\frac{2}{3} by \frac{2}{3} by multiplying y^{2}+\frac{2}{3} by the reciprocal of \frac{2}{3}.

$$x=\frac{3y^{2}}{2}+1$$

Solve for y (complex solution)

$$y=-\frac{\sqrt{6\left(x-1\right)}}{3}$$

$$y=\frac{\sqrt{6\left(x-1\right)}}{3}$$

Solve for y

$$y=\frac{\sqrt{6\left(x-1\right)}}{3}$$

$$y=-\frac{\sqrt{6\left(x-1\right)}}{3}\text{, }x\geq 1$$