Solve 2x^2+5x+2+9*y=0

$$2 { x }^{ 2 } +5x+2+9 \times y = 0$$

Solve for y

$$y=-\frac{\left(x+2\right)\left(2x+1\right)}{9}$$

Steps for Solving Linear Equation

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

$$5x+2+9y=-2x^{2}$$

Subtract 5x from both sides.

$$2+9y=-2x^{2}-5x$$

Subtract 2 from both sides.

$$9y=-2x^{2}-5x-2$$

Divide both sides by 9.

$$\frac{9y}{9}=-\frac{\left(x+2\right)\left(2x+1\right)}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$y=-\frac{\left(x+2\right)\left(2x+1\right)}{9}$$

Solve for x (complex solution)

$$x=\frac{3\sqrt{1-8y}-5}{4}$$

$$x=\frac{-3\sqrt{1-8y}-5}{4}$$

Solve for x

$$x=\frac{3\sqrt{1-8y}-5}{4}$$

$$x=\frac{-3\sqrt{1-8y}-5}{4}\text{, }y\leq \frac{1}{8}$$