Solve 3x+1/2y^2=x

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

Solve for x

$$x=-\frac{y^{2}}{4}$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$3x+\frac{1}{2}y^{2}-x=0$$

Combine 3x and -x to get 2x.

$$2x+\frac{1}{2}y^{2}=0$$

Subtract \frac{1}{2}y^{2} from both sides. Anything subtracted from zero gives its negation.

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

The equation is in standard form.

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

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Divide -\frac{y^{2}}{2} by 2.

$$x=-\frac{y^{2}}{4}$$

Solve for y (complex solution)

$$y=-2i\sqrt{x}$$

$$y=2i\sqrt{x}$$

Solve for y

$$y=2\sqrt{-x}$$

$$y=-2\sqrt{-x}\text{, }x\leq 0$$