Solve y=sqrt{-3x+7}

$$y = \sqrt{ -3x+7 }$$

Solve for x

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

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{-3x+7}=y$$

Square both sides of the equation.

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

Subtract 7 from both sides of the equation.

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

Subtracting 7 from itself leaves 0.

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

Divide both sides by -3.

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

Dividing by -3 undoes the multiplication by -3.

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

Divide y^{2}-7 by -3.

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

Solve for x (complex solution)

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

$$arg(y)<\pi \text{ or }y=0$$

Solve for y (complex solution)

$$y=\sqrt{7-3x}$$

Solve for y

$$y=\sqrt{7-3x}$$

$$x\leq \frac{7}{3}$$