Solve x^2+4y-7x=y

$$x ^ { 2 } + 4 y - 7 x = y$$

Solve for y

$$y=-\frac{x\left(x-7\right)}{3}$$

Steps for Solving Linear Equation

Subtract y from both sides.

$$x^{2}+4y-7x-y=0$$

Combine 4y and -y to get 3y.

$$x^{2}+3y-7x=0$$

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

$$3y-7x=-x^{2}$$

Add 7x to both sides.

$$3y=-x^{2}+7x$$

The equation is in standard form.

$$3y=7x-x^{2}$$

Divide both sides by 3.

$$\frac{3y}{3}=\frac{x\left(7-x\right)}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$y=\frac{x\left(7-x\right)}{3}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{49-12y}+7}{2}$$

$$x=\frac{-\sqrt{49-12y}+7}{2}$$

Solve for x

$$x=\frac{\sqrt{49-12y}+7}{2}$$

$$x=\frac{-\sqrt{49-12y}+7}{2}\text{, }y\leq \frac{49}{12}$$