9x²+24x+16=0

To solve the quadratic equation \(9x^2 + 24x + 16 = 0\), we can use the quadratic formula:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

In this equation, \(a = 9\), \(b = 24\), and \(c = 16\).

1. Calculate the discriminant (\(D\)):

\[ D = b^2 - 4ac = 24^2 - 4 \times 9 \times 16 \] \[ D = 576 - 576 = 0 \]

2. Since the discriminant is 0, there is one real double root. Now substitute the values into the quadratic formula:

\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-24 \pm 0}{2 \times 9} \] \[ x = \frac{-24}{18} = \frac{-4}{3} \]

Therefore, the solution to the equation \(9x^2 + 24x + 16 = 0\) is:

\[ x = -\frac{4}{3} \]

This is the only solution since the discriminant is zero, indicating a double root.