Solve y=-7/23y

$$y = - \frac { 7 } { 23 y }$$

Solve for y

$$y=-\frac{\sqrt{161}i}{23}\approx -0-0.551677284i$$

$$y=\frac{\sqrt{161}i}{23}\approx 0.551677284i$$

Steps by Finding Square Root

Add \frac{7}{23y} to both sides.

$$y+\frac{7}{23y}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{23y}{23y}.

$$\frac{y\times 23y}{23y}+\frac{7}{23y}=0$$

Since \frac{y\times 23y}{23y} and \frac{7}{23y} have the same denominator, add them by adding their numerators.

$$\frac{y\times 23y+7}{23y}=0$$

Do the multiplications in y\times 23y+7.

$$\frac{23y^{2}+7}{23y}=0$$

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 23y.

$$23y^{2}+7=0$$

Subtract 7 from both sides. Anything subtracted from zero gives its negation.

$$23y^{2}=-7$$

Divide both sides by 23.

$$y^{2}=-\frac{7}{23}$$

The equation is now solved.

$$y=\frac{\sqrt{161}i}{23} y=-\frac{\sqrt{161}i}{23}$$

Steps Using the Quadratic Formula

Add \frac{7}{23y} to both sides.

$$y+\frac{7}{23y}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{23y}{23y}.

$$\frac{y\times 23y}{23y}+\frac{7}{23y}=0$$

Since \frac{y\times 23y}{23y} and \frac{7}{23y} have the same denominator, add them by adding their numerators.

$$\frac{y\times 23y+7}{23y}=0$$

Do the multiplications in y\times 23y+7.

$$\frac{23y^{2}+7}{23y}=0$$

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 23y.

$$23y^{2}+7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 23 for a, 0 for b, and 7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 23\times 7}}{2\times 23}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 23\times 7}}{2\times 23}$$

Multiply -4 times 23.

$$y=\frac{0±\sqrt{-92\times 7}}{2\times 23}$$

Multiply -92 times 7.

$$y=\frac{0±\sqrt{-644}}{2\times 23}$$

Take the square root of -644.

$$y=\frac{0±2\sqrt{161}i}{2\times 23}$$

Multiply 2 times 23.

$$y=\frac{0±2\sqrt{161}i}{46}$$

Now solve the equation y=\frac{0±2\sqrt{161}i}{46} when ± is plus.

$$y=\frac{\sqrt{161}i}{23}$$

Now solve the equation y=\frac{0±2\sqrt{161}i}{46} when ± is minus.

$$y=-\frac{\sqrt{161}i}{23}$$

The equation is now solved.

$$y=\frac{\sqrt{161}i}{23} y=-\frac{\sqrt{161}i}{23}$$