Solve 4x^2+6xy+x^2/5=18-4xy

$$4 x ^ { 2 } + 6 x y + \frac { x ^ { 2 } } { 5 } = 18 - 4 x y$$

Solve for y

$$y=-\frac{21x}{50}+\frac{9}{5x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$20x^{2}+30xy+x^{2}=90-20xy$$

Combine 20x^{2} and x^{2} to get 21x^{2}.

$$21x^{2}+30xy=90-20xy$$

Add 20xy to both sides.

$$21x^{2}+30xy+20xy=90$$

Combine 30xy and 20xy to get 50xy.

$$21x^{2}+50xy=90$$

Subtract 21x^{2} from both sides.

$$50xy=90-21x^{2}$$

Divide both sides by 50x.

$$\frac{50xy}{50x}=\frac{90-21x^{2}}{50x}$$

Dividing by 50x undoes the multiplication by 50x.

$$y=\frac{90-21x^{2}}{50x}$$

Divide 90-21x^{2} by 50x.

$$y=-\frac{21x}{50}+\frac{9}{5x}$$

Solve for x

$$x=\frac{\sqrt{625y^{2}+1890}-25y}{21}$$

$$x=\frac{-\sqrt{625y^{2}+1890}-25y}{21}$$