Solve f(x)=x^2-5x+6y(x)=2x

$$f ( x ) = x ^ { 2 } - 5 x + 6 y ( x ) = 2 x$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=\frac{7-x}{6}\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides.

$$-5x+6yx=2x-x^{2}$$

Add 5x to both sides.

$$6yx=2x-x^{2}+5x$$

Combine 2x and 5x to get 7x.

$$6yx=7x-x^{2}$$

The equation is in standard form.

$$6xy=7x-x^{2}$$

Divide both sides by 6x.

$$\frac{6xy}{6x}=\frac{x\left(7-x\right)}{6x}$$

Dividing by 6x undoes the multiplication by 6x.

$$y=\frac{x\left(7-x\right)}{6x}$$

Divide x\left(7-x\right) by 6x.

$$y=\frac{7-x}{6}$$

Solve for y

$$\left\{\begin{matrix}\\y=\frac{7-x}{6}\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides.

$$-5x+6yx=2x-x^{2}$$

Add 5x to both sides.

$$6yx=2x-x^{2}+5x$$

Combine 2x and 5x to get 7x.

$$6yx=7x-x^{2}$$

The equation is in standard form.

$$6xy=7x-x^{2}$$

Divide both sides by 6x.

$$\frac{6xy}{6x}=\frac{x\left(7-x\right)}{6x}$$

Dividing by 6x undoes the multiplication by 6x.

$$y=\frac{x\left(7-x\right)}{6x}$$

Divide x\left(7-x\right) by 6x.

$$y=\frac{7-x}{6}$$

Solve for x

$$x=7-6y$$

$$x=0$$