Solve for x square root of 3x-6 = square root of 5x-4

$\sqrt{3 x - 6} = \sqrt{5 x - 4}$

Step 1

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

${\sqrt{3 x - 6}}^{2} = {\sqrt{5 x - 4}}^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x - 6}$ as ${(3 x - 6)}^{\frac{1}{2}}$ .

${({(3 x - 6)}^{\frac{1}{2}})}^{2} = {\sqrt{5 x - 4}}^{2}$

Simplify the left side.

Simplify ${({(3 x - 6)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(3 x - 6)}^{\frac{1}{2}})}^{2}$ .

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

${(3 x - 6)}^{\frac{1}{2} \cdot 2} = {\sqrt{5 x - 4}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 x - 6)}^{\frac{1}{2} \cdot 2} = {\sqrt{5 x - 4}}^{2}$

Rewrite the expression.

${(3 x - 6)}^{1} = {\sqrt{5 x - 4}}^{2}$

Simplify.

$3 x - 6 = {\sqrt{5 x - 4}}^{2}$

Simplify the right side.

Rewrite ${\sqrt{5 x - 4}}^{2}$ as $5 x - 4$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 x - 4}$ as ${(5 x - 4)}^{\frac{1}{2}}$ .

$3 x - 6 = {({(5 x - 4)}^{\frac{1}{2}})}^{2}$

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

$3 x - 6 = {(5 x - 4)}^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$3 x - 6 = {(5 x - 4)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$3 x - 6 = {(5 x - 4)}^{\frac{2}{2}}$

Rewrite the expression.

$3 x - 6 = {(5 x - 4)}^{1}$

Simplify.

$3 x - 6 = 5 x - 4$

Step 3

Solve for $x$ .

Move all terms containing $x$ to the left side of the equation.

Subtract $5 x$ from both sides of the equation.

$3 x - 6 - 5 x = - 4$

Subtract $5 x$ from $3 x$ .

$- 2 x - 6 = - 4$

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

Add $6$ to both sides of the equation.

$- 2 x = - 4 + 6$

Add $- 4$ and $6$ .

$- 2 x = 2$

Divide each term in $- 2 x = 2$ by $- 2$ and simplify.

Divide each term in $- 2 x = 2$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{2}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{2}{- 2}$

Divide $x$ by $1$ .

$x = \frac{2}{- 2}$

Simplify the right side.

Divide $2$ by $- 2$ .

$x = - 1$

Step 4

Exclude the solutions that do not make $\sqrt{3 x - 6} = \sqrt{5 x - 4}$ true.

$No solution$

Solve for x square root of 3x-6 = square root of 5x-4

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