Solve 3x^2+4y-6=0

$$3 x ^ { 2 } + 4 y - 6 = 0$$

Solve for y

$$y=-\frac{3x^{2}}{4}+\frac{3}{2}$$

Steps for Solving Linear Equation

Subtract 3x^{2} from both sides. Anything subtracted from zero gives its negation.

$$4y-6=-3x^{2}$$

Add 6 to both sides.

$$4y=-3x^{2}+6$$

The equation is in standard form.

$$4y=6-3x^{2}$$

Divide both sides by 4.

$$\frac{4y}{4}=\frac{6-3x^{2}}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$y=\frac{6-3x^{2}}{4}$$

Divide -3x^{2}+6 by 4.

$$y=-\frac{3x^{2}}{4}+\frac{3}{2}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{18-12y}}{3}$$

$$x=\frac{\sqrt{18-12y}}{3}$$

Solve for x

$$x=\frac{\sqrt{18-12y}}{3}$$

$$x=-\frac{\sqrt{18-12y}}{3}\text{, }y\leq \frac{3}{2}$$