In each of the these question two equation (I) and (II) are given. You have to solve both the equtions and give answer accordingly
I `2x^2+9x+9=0`
II `15y^2+16y+4=0`

Options

A. `xgty`
B. `xgey`
C. `xley`
D. `xlty`

Answer

To solve the given equations step by step, we will start with the first equation and then proceed to the second one.

### Step 1: Solve the first equation \(2x^2 + 9x + 9 = 0\)

1. **Identify the coefficients**:
- \(a = 2\), \(b = 9\), \(c = 9\)

2. **Use the quadratic formula**:
The quadratic formula is given by:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

3. **Calculate the discriminant**:
\[ b^2 - 4ac = 9^2 - 4 \cdot 2 \cdot 9 = 81 - 72 = 9 \]

4. **Substitute values into the formula**:
\[ x = \frac{-9 \pm \sqrt{9}}{2 \cdot 2} = \frac{-9 \pm 3}{4} \]

5. **Calculate the two possible values for \(x\)**:
- First value:
\[ x_1 = \frac{-9 + 3}{4} = \frac{-6}{4} = -\frac{3}{2} \]
- Second value:
\[ x_2 = \frac{-9 - 3}{4} = \frac{-12}{4} = -3 \]

### Step 2: Solve the second equation \(15y^2 + 16y + 4 = 0\)

1. **Identify the coefficients**:
- \(a = 15\), \(b = 16\), \(c = 4\)

2. **Use the quadratic formula**:
\[ y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

3. **Calculate the discriminant**:
\[ b^2 - 4ac = 16^2 - 4 \cdot 15 \cdot 4 = 256 - 240 = 16 \]

4. **Substitute values into the formula**:
\[ y = \frac{-16 \pm \sqrt{16}}{2 \cdot 15} = \frac{-16 \pm 4}{30} \]

5. **Calculate the two possible values for \(y\)**:
- First value:
\[ y_1 = \frac{-16 + 4}{30} = \frac{-12}{30} = -\frac{2}{5} \]
- Second value:
\[ y_2 = \frac{-16 - 4}{30} = \frac{-20}{30} = -\frac{2}{3} \]

### Summary of Solutions
- For the first equation \(2x^2 + 9x + 9 = 0\), the solutions are:
- \(x_1 = -\frac{3}{2}\)
- \(x_2 = -3\)

- For the second equation \(15y^2 + 16y + 4 = 0\), the solutions are:
- \(y_1 = -\frac{2}{5}\)
- \(y_2 = -\frac{2}{3}\)