Solve -3+left(3x-5right)^2=0

$$-3+ { \left(3x-5 \right) }^{ 2 } =0$$

Solve for x

$$x = \frac{\sqrt{3} + 5}{3} \approx 2.244016936$$

$$x = \frac{5 - \sqrt{3}}{3} \approx 1.089316397$$

Steps by Finding Square Root

Add 3 to both sides of the equation.

$$\left(3x-5\right)^{2}-3+3=3$$

Subtracting 3 from itself leaves 0.

$$\left(3x-5\right)^{2}=3$$

Take the square root of both sides of the equation.

$$3x-5=\sqrt{3} 3x-5=-\sqrt{3}$$

Add 5 to both sides of the equation.

$$3x-5-\left(-5\right)=\sqrt{3}-\left(-5\right) 3x-5-\left(-5\right)=-\sqrt{3}-\left(-5\right)$$

Subtracting -5 from itself leaves 0.

$$3x=\sqrt{3}-\left(-5\right) 3x=-\sqrt{3}-\left(-5\right)$$

Subtract -5 from \sqrt{3}.

$$3x=\sqrt{3}+5$$

Subtract -5 from -\sqrt{3}.

$$3x=5-\sqrt{3}$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{\sqrt{3}+5}{3} \frac{3x}{3}=\frac{5-\sqrt{3}}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{\sqrt{3}+5}{3} x=\frac{5-\sqrt{3}}{3}$$