Solve 2x^2+5x+6y=60xy

$$2 x ^ { 2 } + 5 x + 6 y = 60 x y$$

Solve for y

$$y=-\frac{x\left(2x+5\right)}{6\left(1-10x\right)}$$

$$x\neq \frac{1}{10}$$

Steps for Solving Linear Equation

Subtract 60xy from both sides.

$$2x^{2}+5x+6y-60xy=0$$

Subtract 2x^{2} from both sides. Anything subtracted from zero gives its negation.

$$5x+6y-60xy=-2x^{2}$$

Subtract 5x from both sides.

$$6y-60xy=-2x^{2}-5x$$

Combine all terms containing y.

$$\left(6-60x\right)y=-2x^{2}-5x$$

Divide both sides by 6-60x.

$$\frac{\left(6-60x\right)y}{6-60x}=-\frac{x\left(2x+5\right)}{6-60x}$$

Dividing by 6-60x undoes the multiplication by 6-60x.

$$y=-\frac{x\left(2x+5\right)}{6-60x}$$

Divide -x\left(5+2x\right) by 6-60x.

$$y=-\frac{x\left(2x+5\right)}{6\left(1-10x\right)}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{3600y^{2}-648y+25}}{4}+15y-\frac{5}{4}$$

$$x=-\frac{\sqrt{3600y^{2}-648y+25}}{4}+15y-\frac{5}{4}$$

Solve for x

$$x=\frac{\sqrt{3600y^{2}-648y+25}}{4}+15y-\frac{5}{4}$$

$$x=-\frac{\sqrt{3600y^{2}-648y+25}}{4}+15y-\frac{5}{4}\text{, }y\geq \frac{\sqrt{26}}{150}+\frac{9}{100}\text{ or }y\leq -\frac{\sqrt{26}}{150}+\frac{9}{100}$$