Solve x^2=(3x-y+1)

$$x ^ { 2 } = ( 3 x - y + 1 )$$

Solve for y

$$y=1+3x-x^{2}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$3x-y+1=x^{2}$$

Subtract 3x from both sides.

$$-y+1=x^{2}-3x$$

Subtract 1 from both sides.

$$-y=x^{2}-3x-1$$

Divide both sides by -1.

$$\frac{-y}{-1}=\frac{x^{2}-3x-1}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$y=\frac{x^{2}-3x-1}{-1}$$

Divide x^{2}-3x-1 by -1.

$$y=1+3x-x^{2}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{13-4y}+3}{2}$$

$$x=\frac{-\sqrt{13-4y}+3}{2}$$

Solve for x

$$x=\frac{\sqrt{13-4y}+3}{2}$$

$$x=\frac{-\sqrt{13-4y}+3}{2}\text{, }y\leq \frac{13}{4}$$