Solve 2x^2+4x-9y=20

$$2 { x }^{ 2 } +4x-9y=20$$

Solve for y

$$y=\frac{2\left(x^{2}+2x-10\right)}{9}$$

Steps for Solving Linear Equation

Subtract 2x^{2} from both sides.

$$4x-9y=20-2x^{2}$$

Subtract 4x from both sides.

$$-9y=20-2x^{2}-4x$$

The equation is in standard form.

$$-9y=20-4x-2x^{2}$$

Divide both sides by -9.

$$\frac{-9y}{-9}=\frac{20-4x-2x^{2}}{-9}$$

Dividing by -9 undoes the multiplication by -9.

$$y=\frac{20-4x-2x^{2}}{-9}$$

Divide 20-2x^{2}-4x by -9.

$$y=\frac{2x^{2}+4x-20}{9}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{18y+44}}{2}-1$$

$$x=-\frac{\sqrt{18y+44}}{2}-1$$

Solve for x

$$x=\frac{\sqrt{18y+44}}{2}-1$$

$$x=-\frac{\sqrt{18y+44}}{2}-1\text{, }y\geq -\frac{22}{9}$$