Solve for y (5y-3)^2=9

${(5 y - 3)}^{2} = 9$

Step 1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$5 y - 3 = \pm \sqrt{9}$

Step 2

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

$5 y - 3 = \pm \sqrt{3^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$5 y - 3 = \pm 3$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$5 y - 3 = 3$

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

Add $3$ to both sides of the equation.

$5 y = 3 + 3$

Add $3$ and $3$ .

$5 y = 6$

Divide each term in $5 y = 6$ by $5$ and simplify.

Divide each term in $5 y = 6$ by $5$ .

$\frac{5 y}{5} = \frac{6}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{6}{5}$

Divide $y$ by $1$ .

$y = \frac{6}{5}$

Next, use the negative value of the $\pm$ to find the second solution.

$5 y - 3 = - 3$

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

Add $3$ to both sides of the equation.

$5 y = - 3 + 3$

Add $- 3$ and $3$ .

$5 y = 0$

Divide each term in $5 y = 0$ by $5$ and simplify.

Divide each term in $5 y = 0$ by $5$ .

$\frac{5 y}{5} = \frac{0}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{0}{5}$

Divide $y$ by $1$ .

$y = \frac{0}{5}$

Simplify the right side.

Divide $0$ by $5$ .

$y = 0$

The complete solution is the result of both the positive and negative portions of the solution.

$y = \frac{6}{5}, 0$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{6}{5}, 0$

Decimal Form:

$y = 1.2, 0$

Mixed Number Form:

$y = 1 \frac{1}{5}, 0$

Solve for y (5y-3)^2=9

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