How to solve 9/(2y) = y/8

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve 9/(2y) = y/8 | Equatix

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Question

$$\frac{9}{2y}=\frac{y}{8}$$

Solve for y

$y=6$
$y=-6$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Variable $y$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $8y$, the least common multiple of $2y,8$.

$$4\times 9=yy$$

Multiply $y$ and $y$ to get $y^{2}$.

$$4\times 9=y^{2}$$

Multiply $4$ and $9$ to get $36$.

$$36=y^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$y^{2}=36$$

Take the square root of both sides of the equation.

$$y=6$$ $$y=-6$$

Steps Using the Quadratic Formula

Variable $y$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $8y$, the least common multiple of $2y,8$.

$$4\times 9=yy$$

Multiply $y$ and $y$ to get $y^{2}$.

$$4\times 9=y^{2}$$

Multiply $4$ and $9$ to get $36$.

$$36=y^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$y^{2}=36$$

Subtract $36$ from both sides.

$$y^{2}-36=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-36$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$y=\frac{0±\sqrt{0^{2}-4\left(-36\right)}}{2}$$

Square $0$.

$$y=\frac{0±\sqrt{-4\left(-36\right)}}{2}$$

Multiply $-4$ times $-36$.

$$y=\frac{0±\sqrt{144}}{2}$$

Take the square root of $144$.

$$y=\frac{0±12}{2}$$

Now solve the equation $y=\frac{0±12}{2}$ when $±$ is plus. Divide $12$ by $2$.

$$y=6$$

Now solve the equation $y=\frac{0±12}{2}$ when $±$ is minus. Divide $-12$ by $2$.

$$y=-6$$

The equation is now solved.

$$y=6$$ $$y=-6$$

Show Solution

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Example

Question

Solve for y

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Steps Using the Quadratic Formula