Solve 2x^2+3x+2y=10

$$2 x ^ { 2 } + 3 x + 2 y = 10$$

Solve for y

$$y=-x^{2}-\frac{3x}{2}+5$$

Steps for Solving Linear Equation

Subtract 2x^{2} from both sides.

$$3x+2y=10-2x^{2}$$

Subtract 3x from both sides.

$$2y=10-2x^{2}-3x$$

The equation is in standard form.

$$2y=10-3x-2x^{2}$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{10-3x-2x^{2}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{10-3x-2x^{2}}{2}$$

Divide 10-2x^{2}-3x by 2.

$$y=-x^{2}-\frac{3x}{2}+5$$

Solve for x (complex solution)

$$x=\frac{\sqrt{89-16y}-3}{4}$$

$$x=\frac{-\sqrt{89-16y}-3}{4}$$

Solve for x

$$x=\frac{\sqrt{89-16y}-3}{4}$$

$$x=\frac{-\sqrt{89-16y}-3}{4}\text{, }y\leq \frac{89}{16}$$