Solve 9(3-y)^2=4

$$9 ( 3 - y ) ^ { 2 } = 4$$

Solve for y

$$y = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333$$

$$y = \frac{11}{3} = 3\frac{2}{3} \approx 3.666666667$$

Steps by Finding Square Root

Divide both sides by 9.

$$\frac{9\left(-y+3\right)^{2}}{9}=\frac{4}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$\left(-y+3\right)^{2}=\frac{4}{9}$$

Take the square root of both sides of the equation.

$$-y+3=\frac{2}{3} -y+3=-\frac{2}{3}$$

Subtract 3 from both sides of the equation.

$$-y+3-3=\frac{2}{3}-3 -y+3-3=-\frac{2}{3}-3$$

Subtracting 3 from itself leaves 0.

$$-y=\frac{2}{3}-3 -y=-\frac{2}{3}-3$$

Subtract 3 from \frac{2}{3}.

$$-y=-\frac{7}{3}$$

Subtract 3 from -\frac{2}{3}.

$$-y=-\frac{11}{3}$$

Divide both sides by -1.

$$\frac{-y}{-1}=-\frac{\frac{7}{3}}{-1} \frac{-y}{-1}=-\frac{\frac{11}{3}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$y=-\frac{\frac{7}{3}}{-1} y=-\frac{\frac{11}{3}}{-1}$$

Divide -\frac{7}{3} by -1.

$$y=\frac{7}{3}$$

Divide -\frac{11}{3} by -1.

$$y=\frac{11}{3}$$

The equation is now solved.

$$y=\frac{7}{3} y=\frac{11}{3}$$