Solve sqrt{4(x-1)/5}-6=0

$$\sqrt { \frac { 4 ( x - 1 ) } { 5 } } - 6 = 0$$

Solve for x

$$x=46$$

Steps for Solving Radical Equations

Use the distributive property to multiply 4 by x-1.

$$\sqrt{\frac{4x-4}{5}}-6=0$$

Divide each term of 4x-4 by 5 to get \frac{4}{5}x-\frac{4}{5}.

$$\sqrt{\frac{4}{5}x-\frac{4}{5}}-6=0$$

Add 6 to both sides. Anything plus zero gives itself.

$$\sqrt{\frac{4}{5}x-\frac{4}{5}}=6$$

Square both sides of the equation.

$$\frac{4}{5}x-\frac{4}{5}=36$$

Add \frac{4}{5} to both sides of the equation.

$$\frac{4}{5}x-\frac{4}{5}-\left(-\frac{4}{5}\right)=36-\left(-\frac{4}{5}\right)$$

Subtracting -\frac{4}{5} from itself leaves 0.

$$\frac{4}{5}x=36-\left(-\frac{4}{5}\right)$$

Subtract -\frac{4}{5} from 36.

$$\frac{4}{5}x=\frac{184}{5}$$

Divide both sides of the equation by \frac{4}{5}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{4}{5}x}{\frac{4}{5}}=\frac{\frac{184}{5}}{\frac{4}{5}}$$

Dividing by \frac{4}{5} undoes the multiplication by \frac{4}{5}.

$$x=\frac{\frac{184}{5}}{\frac{4}{5}}$$

Divide \frac{184}{5} by \frac{4}{5} by multiplying \frac{184}{5} by the reciprocal of \frac{4}{5}.

$$x=46$$