Solve this equation by using the quadratic formula $$ x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a} $$, and select the choice that contains all of the solutions. $$ 2 x^{2}+5 x-5=0 $$

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To solve the quadratic equation $$ 2x^{2} + 5x - 5 = 0 $$ using the quadratic formula:

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

**Step 1: Identify the coefficients**

$$
a = 2,\quad b = 5,\quad c = -5
$$

**Step 2: Calculate the discriminant ($$ \Delta $$)**

$$
\Delta = b^{2} - 4ac = 5^{2} - 4(2)(-5) = 25 + 40 = 65
$$

**Step 3: Apply the quadratic formula**

$$
x = \frac{-5 \pm \sqrt{65}}{2 \times 2} = \frac{-5 \pm \sqrt{65}}{4}
$$

**Solutions:**

$$
x = \frac{-5 + \sqrt{65}}{4} \quad \text{and} \quad x = \frac{-5 - \sqrt{65}}{4}
$$

These two values are the solutions to the quadratic equation $$ 2x^{2} + 5x - 5 = 0 $$.
The solutions are $$ x = \frac{-5 + \sqrt{65}}{4} $$ and $$ x = \frac{-5 - \sqrt{65}}{4} $$.

Solve this equation by using the quadratic formula \( x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a} \), and select the choice that contains all of the solutions. \[ 2 x^{2}+5 x-5=0 \]

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