Solve 3left(x-2right)^2-2=0

$$3 { \left(x-2 \right) }^{ 2 } -2=0$$

Solve for x

$$x=\frac{\sqrt{6}}{3}+2\approx 2.816496581$$

$$x=-\frac{\sqrt{6}}{3}+2\approx 1.183503419$$

Steps by Finding Square Root

Add 2 to both sides of the equation.

$$3\left(x-2\right)^{2}-2+2=2$$

Subtracting 2 from itself leaves 0.

$$3\left(x-2\right)^{2}=2$$

Divide both sides by 3.

$$\frac{3\left(x-2\right)^{2}}{3}=\frac{2}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$\left(x-2\right)^{2}=\frac{2}{3}$$

Take the square root of both sides of the equation.

$$x-2=\frac{\sqrt{6}}{3} x-2=-\frac{\sqrt{6}}{3}$$

Add 2 to both sides of the equation.

$$x-2-\left(-2\right)=\frac{\sqrt{6}}{3}-\left(-2\right) x-2-\left(-2\right)=-\frac{\sqrt{6}}{3}-\left(-2\right)$$

Subtracting -2 from itself leaves 0.

$$x=\frac{\sqrt{6}}{3}-\left(-2\right) x=-\frac{\sqrt{6}}{3}-\left(-2\right)$$

Subtract -2 from \frac{\sqrt{6}}{3}.

$$x=\frac{\sqrt{6}}{3}+2$$

Subtract -2 from -\frac{\sqrt{6}}{3}.

$$x=-\frac{\sqrt{6}}{3}+2$$

The equation is now solved.

$$x=\frac{\sqrt{6}}{3}+2 x=-\frac{\sqrt{6}}{3}+2$$