$$ = \frac { - 2 \pm \sqrt { 20 } } { 4 } $$

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To solve the expression $$ x = \frac{-2 \pm \sqrt{20}}{4} $$, we will break it down step by step.

1. **Calculate the square root**: First, we need to simplify $$ \sqrt{20} $$.
   $$
   \sqrt{20} = \sqrt{4 \cdot 5} = \sqrt{4} \cdot \sqrt{5} = 2\sqrt{5}
   $$

2. **Substitute back into the expression**: Now we can substitute $$ \sqrt{20} $$ back into the equation.
   $$
   x = \frac{-2 \pm 2\sqrt{5}}{4}
   $$

3. **Simplify the expression**: We can simplify the fraction by dividing each term in the numerator by 2.
   $$
   x = \frac{-2}{4} \pm \frac{2\sqrt{5}}{4} = \frac{-1}{2} \pm \frac{\sqrt{5}}{2}
   $$

4. **Final result**: Thus, we can express the solutions as:
   $$
   x = \frac{-1 + \sqrt{5}}{2} \quad \text{and} \quad x = \frac{-1 - \sqrt{5}}{2}
   $$

These are the two possible values for $$ x $$.
$$ x = \frac{-1 + \sqrt{5}}{2} $$ or $$ x = \frac{-1 - \sqrt{5}}{2} $$

\( = \frac { - 2 \pm \sqrt { 20 } } { 4 } \)

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