Solve for y. y-13=-9+(21)/(y) If there is more than one solution separate them with commas. If there is no solution, click on "No solution". y= square

To solve the equation \( y - 13 = -9 + \frac{21}{y} \), we first eliminate the fraction by multiplying both sides of the equation by \( y \):<br /><br />\[ y(y - 13) = y(-9 + \frac{21}{y}) \]<br /><br />This simplifies to:<br /><br />\[ y^2 - 13y = -9y + 21 \]<br /><br />Next, we move all terms to one side of the equation to set it to zero:<br /><br />\[ y^2 - 13y + 9y - 21 = 0 \]<br /><br />Combine like terms:<br /><br />\[ y^2 - 4y - 21 = 0 \]<br /><br />Now, we solve this quadratic equation using the quadratic formula \( y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = -4 \), and \( c = -21 \):<br /><br />\[ y = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(-21)}}{2(1)} \]<br /><br />\[ y = \frac{4 \pm \sqrt{16 + 84}}{2} \]<br /><br />\[ y = \frac{4 \pm \sqrt{100}}{2} \]<br /><br />\[ y = \frac{4 \pm 10}{2} \]<br /><br />This gives us two solutions:<br /><br />\[ y = \frac{4 + 10}{2} = \frac{14}{2} = 7 \]<br /><br />\[ y = \frac{4 - 10}{2} = \frac{-6}{2} = -3 \]<br /><br />So, the solutions are:<br /><br />\[ y = 7, -3 \]