Find All Complex Solutions square root of 6x-4=3

$\sqrt{6 x - 4} = 3$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{6 x - 4}}^{2} = 3^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6 x - 4}$ as ${(6 x - 4)}^{\frac{1}{2}}$ .

${({(6 x - 4)}^{\frac{1}{2}})}^{2} = 3^{2}$

Simplify the left side.

Simplify ${({(6 x - 4)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(6 x - 4)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(6 x - 4)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(6 x - 4)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Rewrite the expression.

${(6 x - 4)}^{1} = 3^{2}$

Simplify.

$6 x - 4 = 3^{2}$

Simplify the right side.

Raise $3$ to the power of $2$ .

$6 x - 4 = 9$

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Add $4$ to both sides of the equation.

$6 x = 9 + 4$

Add $9$ and $4$ .

$6 x = 13$

Divide each term in $6 x = 13$ by $6$ and simplify.

Divide each term in $6 x = 13$ by $6$ .

$\frac{6 x}{6} = \frac{13}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{13}{6}$

Divide $x$ by $1$ .

$x = \frac{13}{6}$