Solve y/3=27/y

$$\frac { y } { 3 } = \frac { 27 } { y }$$

Solve for y

$$y=9$$

$$y=-9$$

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 3y, the least common multiple of 3,y.

$$yy=3\times 27$$

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

$$y^{2}=3\times 27$$

Multiply 3 and 27 to get 81.

$$y^{2}=81$$

Take the square root of both sides of the equation.

$$y=9 y=-9$$

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 3y, the least common multiple of 3,y.

$$yy=3\times 27$$

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

$$y^{2}=3\times 27$$

Multiply 3 and 27 to get 81.

$$y^{2}=81$$

Subtract 81 from both sides.

$$y^{2}-81=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -81 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-81\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-81\right)}}{2}$$

Multiply -4 times -81.

$$y=\frac{0±\sqrt{324}}{2}$$

Take the square root of 324.

$$y=\frac{0±18}{2}$$

Now solve the equation y=\frac{0±18}{2} when ± is plus. Divide 18 by 2.

$$y=9$$

Now solve the equation y=\frac{0±18}{2} when ± is minus. Divide -18 by 2.

$$y=-9$$

The equation is now solved.

$$y=9 y=-9$$