Solve 7y^2+15xy=-68

$$7 { y }^{ 2 } +15xy = -68$$

Solve for x

$$x=-\frac{7y}{15}-\frac{68}{15y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Subtract 7y^{2} from both sides.

$$15xy=-68-7y^{2}$$

The equation is in standard form.

$$15yx=-7y^{2}-68$$

Divide both sides by 15y.

$$\frac{15yx}{15y}=\frac{-7y^{2}-68}{15y}$$

Dividing by 15y undoes the multiplication by 15y.

$$x=\frac{-7y^{2}-68}{15y}$$

Divide -68-7y^{2} by 15y.

$$x=-\frac{7y}{15}-\frac{68}{15y}$$

Solve for y (complex solution)

$$y=\frac{\sqrt{225x^{2}-1904}-15x}{14}$$

$$y=\frac{-\sqrt{225x^{2}-1904}-15x}{14}$$

Solve for y

$$y=\frac{\sqrt{225x^{2}-1904}-15x}{14}$$

$$y=\frac{-\sqrt{225x^{2}-1904}-15x}{14}\text{, }|x|\geq \frac{4\sqrt{119}}{15}$$