Solve 3x^2-6x+3y-7=0

$$3 x ^ { 2 } - 6 x + 3 y - 7 = 0$$

Solve for y

$$y=\frac{7}{3}+2x-x^{2}$$

Steps for Solving Linear Equation

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

$$-6x+3y-7=-3x^{2}$$

Add 6x to both sides.

$$3y-7=-3x^{2}+6x$$

Add 7 to both sides.

$$3y=-3x^{2}+6x+7$$

The equation is in standard form.

$$3y=7+6x-3x^{2}$$

Divide both sides by 3.

$$\frac{3y}{3}=\frac{7+6x-3x^{2}}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$y=\frac{7+6x-3x^{2}}{3}$$

Divide -3x^{2}+6x+7 by 3.

$$y=\frac{7}{3}+2x-x^{2}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{30-9y}}{3}+1$$

$$x=-\frac{\sqrt{30-9y}}{3}+1$$

Solve for x

$$x=\frac{\sqrt{30-9y}}{3}+1$$

$$x=-\frac{\sqrt{30-9y}}{3}+1\text{, }y\leq \frac{10}{3}$$