Solve 4x+7=3y-2+7x^2

$$4 x + 7 = 3 y - 2 + 7 x ^ { 2 }$$

Solve for y

$$y=-\frac{7x^{2}}{3}+\frac{4x}{3}+3$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$3y-2+7x^{2}=4x+7$$

Add 2 to both sides.

$$3y+7x^{2}=4x+7+2$$

Add 7 and 2 to get 9.

$$3y+7x^{2}=4x+9$$

Subtract 7x^{2} from both sides.

$$3y=4x+9-7x^{2}$$

The equation is in standard form.

$$3y=9+4x-7x^{2}$$

Divide both sides by 3.

$$\frac{3y}{3}=\frac{9+4x-7x^{2}}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$y=\frac{9+4x-7x^{2}}{3}$$

Divide 4x+9-7x^{2} by 3.

$$y=-\frac{7x^{2}}{3}+\frac{4x}{3}+3$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{67-21y}+2}{7}$$

$$x=\frac{\sqrt{67-21y}+2}{7}$$

Solve for x

$$x=\frac{-\sqrt{67-21y}+2}{7}$$

$$x=\frac{\sqrt{67-21y}+2}{7}\text{, }y\leq \frac{67}{21}$$