Solve 5x^2-3x+5y=36y

$$5 x ^ { 2 } - 3 x + 5 y = 36 y$$

Solve for y

$$y=\frac{x\left(5x-3\right)}{31}$$

Steps for Solving Linear Equation

Subtract 36y from both sides.

$$5x^{2}-3x+5y-36y=0$$

Combine 5y and -36y to get -31y.

$$5x^{2}-3x-31y=0$$

Subtract 5x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-3x-31y=-5x^{2}$$

Add 3x to both sides.

$$-31y=-5x^{2}+3x$$

The equation is in standard form.

$$-31y=3x-5x^{2}$$

Divide both sides by -31.

$$\frac{-31y}{-31}=\frac{x\left(3-5x\right)}{-31}$$

Dividing by -31 undoes the multiplication by -31.

$$y=\frac{x\left(3-5x\right)}{-31}$$

Divide x\left(3-5x\right) by -31.

$$y=-\frac{x\left(3-5x\right)}{31}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{620y+9}+3}{10}$$

$$x=\frac{-\sqrt{620y+9}+3}{10}$$

Solve for x

$$x=\frac{\sqrt{620y+9}+3}{10}$$

$$x=\frac{-\sqrt{620y+9}+3}{10}\text{, }y\geq -\frac{9}{620}$$