Solve (4y-1)^2-6=0

$$( 4 y - 1 ) ^ { 2 } - 6 = 0$$

Solve for y

$$y=\frac{\sqrt{6}+1}{4}\approx 0.862372436$$

$$y=\frac{1-\sqrt{6}}{4}\approx -0.362372436$$

Steps by Finding Square Root

Add 6 to both sides of the equation.

$$\left(4y-1\right)^{2}-6+6=6$$

Subtracting 6 from itself leaves 0.

$$\left(4y-1\right)^{2}=6$$

Take the square root of both sides of the equation.

$$4y-1=\sqrt{6} 4y-1=-\sqrt{6}$$

Add 1 to both sides of the equation.

$$4y-1-\left(-1\right)=\sqrt{6}-\left(-1\right) 4y-1-\left(-1\right)=-\sqrt{6}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$4y=\sqrt{6}-\left(-1\right) 4y=-\sqrt{6}-\left(-1\right)$$

Subtract -1 from \sqrt{6}.

$$4y=\sqrt{6}+1$$

Subtract -1 from -\sqrt{6}.

$$4y=1-\sqrt{6}$$

Divide both sides by 4.

$$\frac{4y}{4}=\frac{\sqrt{6}+1}{4} \frac{4y}{4}=\frac{1-\sqrt{6}}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$y=\frac{\sqrt{6}+1}{4} y=\frac{1-\sqrt{6}}{4}$$