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

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

Solve for y

$$y=3\left(2x^{2}+x-2\right)$$

Steps for Solving Linear Equation

Subtract 6x^{2} from both sides.

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

Subtract 3x from both sides.

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

The equation is in standard form.

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

Divide both sides by -1.

$$\frac{-y}{-1}=\frac{6-3x-6x^{2}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$y=\frac{6-3x-6x^{2}}{-1}$$

Divide 6-6x^{2}-3x by -1.

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

Solve for x (complex solution)

$$x=\frac{\sqrt{24y+153}}{12}-\frac{1}{4}$$

$$x=-\frac{\sqrt{24y+153}}{12}-\frac{1}{4}$$

Solve for x

$$x=\frac{\sqrt{24y+153}}{12}-\frac{1}{4}$$

$$x=-\frac{\sqrt{24y+153}}{12}-\frac{1}{4}\text{, }y\geq -\frac{51}{8}$$