Solve 2x^2=3(y+1)

$$2 x ^ { 2 } = 3 ( y + 1 )$$

Solve for y

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

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by y+1.

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

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

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

Subtract 3 from both sides.

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

Divide both sides by 3.

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

Dividing by 3 undoes the multiplication by 3.

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

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

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

Solve for x (complex solution)

$$x=-\frac{\sqrt{6\left(y+1\right)}}{2}$$

$$x=\frac{\sqrt{6\left(y+1\right)}}{2}$$

Solve for x

$$x=\frac{\sqrt{6\left(y+1\right)}}{2}$$

$$x=-\frac{\sqrt{6\left(y+1\right)}}{2}\text{, }y\geq -1$$