Solve 212x+3y/2^2+y^2=9

$$\frac { 212 x + 3 y } { 2 ^ { 2 } + y ^ { 2 } } = 9$$

Solve for x (complex solution)

$$x=\frac{9y^{2}}{212}-\frac{3y}{212}+\frac{9}{53}$$

$$y\neq -2i\text{ and }y\neq 2i$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(y-2i\right)\left(y+2i\right).

$$212x+3y=9\left(y-2i\right)\left(y+2i\right)$$

Use the distributive property to multiply 9 by y-2i.

$$212x+3y=\left(9y-18i\right)\left(y+2i\right)$$

Use the distributive property to multiply 9y-18i by y+2i and combine like terms.

$$212x+3y=9y^{2}+36$$

Subtract 3y from both sides.

$$212x=9y^{2}+36-3y$$

The equation is in standard form.

$$212x=9y^{2}-3y+36$$

Divide both sides by 212.

$$\frac{212x}{212}=\frac{9y^{2}-3y+36}{212}$$

Dividing by 212 undoes the multiplication by 212.

$$x=\frac{9y^{2}-3y+36}{212}$$

Divide 9y^{2}+36-3y by 212.

$$x=\frac{9y^{2}}{212}-\frac{3y}{212}+\frac{9}{53}$$

Solve for x

$$x=\frac{9y^{2}}{212}-\frac{3y}{212}+\frac{9}{53}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y^{2}+4.

$$212x+3y=9\left(y^{2}+4\right)$$

Use the distributive property to multiply 9 by y^{2}+4.

$$212x+3y=9y^{2}+36$$

Subtract 3y from both sides.

$$212x=9y^{2}+36-3y$$

The equation is in standard form.

$$212x=9y^{2}-3y+36$$

Divide both sides by 212.

$$\frac{212x}{212}=\frac{9y^{2}-3y+36}{212}$$

Dividing by 212 undoes the multiplication by 212.

$$x=\frac{9y^{2}-3y+36}{212}$$

Divide 9y^{2}+36-3y by 212.

$$x=\frac{9y^{2}}{212}-\frac{3y}{212}+\frac{9}{53}$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=\frac{\sqrt{848x-143}+1}{6}\text{, }&\text{unconditionally}\\y=\frac{-\sqrt{848x-143}+1}{6}\text{, }&x\neq \frac{3}{106}i\text{ and }x\neq -\frac{3}{106}i\end{matrix}\right.$$

Solve for y

$$y=\frac{-\sqrt{848x-143}+1}{6}$$

$$y=\frac{\sqrt{848x-143}+1}{6}\text{, }x\geq \frac{143}{848}$$