Solve 2x^2+6y+42=89

$$2 x ^ { 2 } + 6 y + 42 = 89$$

Solve for y

$$y=-\frac{x^{2}}{3}+\frac{47}{6}$$

Steps for Solving Linear Equation

Subtract 2x^{2} from both sides.

$$6y+42=89-2x^{2}$$

Subtract 42 from both sides.

$$6y=89-2x^{2}-42$$

Subtract 42 from 89 to get 47.

$$6y=47-2x^{2}$$

Divide both sides by 6.

$$\frac{6y}{6}=\frac{47-2x^{2}}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$y=\frac{47-2x^{2}}{6}$$

Divide 47-2x^{2} by 6.

$$y=-\frac{x^{2}}{3}+\frac{47}{6}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{94-12y}}{2}$$

$$x=\frac{\sqrt{94-12y}}{2}$$

Solve for x

$$x=\frac{\sqrt{94-12y}}{2}$$

$$x=-\frac{\sqrt{94-12y}}{2}\text{, }y\leq \frac{47}{6}$$