Solve the Quadratic Equation: 9y² - 30y = -25

To solve the quadratic equation $9y^2 - 30y = -25$, we first rewrite it in standard form:

$9y^2 - 30y + 25 = 0$.

Identifying the coefficients, we have $a = 9$, $b = -30$, and $c = 25$. We will apply the quadratic formula:

$y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

First, compute the discriminant:

$b^2 - 4ac = (-30)^2 - 4 \cdot 9 \cdot 25 = 900 - 900 = 0$.

Since the discriminant is zero, there is a single repeated root. Substituting back into the quadratic formula, we get:

$y = \frac{-(-30) \pm \sqrt{0}}{2 \cdot 9} = \frac{30}{18} = \frac{5}{3}$.

Therefore, the solution to the equation is $y = \frac{5}{3}$.