Solve (4x-3)^2=5

$$( 4 x - 3 ) ^ { 2 } = 5$$

Solve for x

$$x = \frac{\sqrt{5} + 3}{4} \approx 1.309016994$$

$$x=\frac{3-\sqrt{5}}{4}\approx 0.190983006$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$4x-3=\sqrt{5} 4x-3=-\sqrt{5}$$

Add 3 to both sides of the equation.

$$4x-3-\left(-3\right)=\sqrt{5}-\left(-3\right) 4x-3-\left(-3\right)=-\sqrt{5}-\left(-3\right)$$

Subtracting -3 from itself leaves 0.

$$4x=\sqrt{5}-\left(-3\right) 4x=-\sqrt{5}-\left(-3\right)$$

Subtract -3 from \sqrt{5}.

$$4x=\sqrt{5}+3$$

Subtract -3 from -\sqrt{5}.

$$4x=3-\sqrt{5}$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{\sqrt{5}+3}{4} \frac{4x}{4}=\frac{3-\sqrt{5}}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{\sqrt{5}+3}{4} x=\frac{3-\sqrt{5}}{4}$$