Solve 3(2x-3)^2=54

$$3 ( 2 x - 3 ) ^ { 2 } = 54$$

Solve for x

$$x = \frac{3 \sqrt{2} + 3}{2} \approx 3.621320344$$

$$x=\frac{3-3\sqrt{2}}{2}\approx -0.621320344$$

Steps by Finding Square Root

Divide both sides by 3.

$$\frac{3\left(2x-3\right)^{2}}{3}=\frac{54}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$\left(2x-3\right)^{2}=\frac{54}{3}$$

Divide 54 by 3.

$$\left(2x-3\right)^{2}=18$$

Take the square root of both sides of the equation.

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

Add 3 to both sides of the equation.

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

Subtracting -3 from itself leaves 0.

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

Subtract -3 from 3\sqrt{2}.

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

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

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

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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