Solve 5/y=y/8

$$\frac { 5 } { y } = \frac { y } { 8 }$$

Solve for y

$$y=2\sqrt{10}\approx 6.32455532$$

$$y=-2\sqrt{10}\approx -6.32455532$$

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 y,8.

$$8\times 5=yy$$

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

$$8\times 5=y^{2}$$

Multiply 8 and 5 to get 40.

$$40=y^{2}$$

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

$$y^{2}=40$$

Take the square root of both sides of the equation.

$$y=2\sqrt{10} y=-2\sqrt{10}$$

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 y,8.

$$8\times 5=yy$$

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

$$8\times 5=y^{2}$$

Multiply 8 and 5 to get 40.

$$40=y^{2}$$

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

$$y^{2}=40$$

Subtract 40 from both sides.

$$y^{2}-40=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -40 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-40\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-40\right)}}{2}$$

Multiply -4 times -40.

$$y=\frac{0±\sqrt{160}}{2}$$

Take the square root of 160.

$$y=\frac{0±4\sqrt{10}}{2}$$

Now solve the equation y=\frac{0±4\sqrt{10}}{2} when ± is plus.

$$y=2\sqrt{10}$$

Now solve the equation y=\frac{0±4\sqrt{10}}{2} when ± is minus.

$$y=-2\sqrt{10}$$

The equation is now solved.

$$y=2\sqrt{10} y=-2\sqrt{10}$$