x2-2x-4=0

To solve the quadratic equation \( x^2 - 2x - 4 = 0 \) using the quadratic formula, we can use the formula:

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

For the given equation, the coefficients are:

• \( a = 1 \)
• \( b = -2 \)
• \( c = -4 \)

First, we will calculate the discriminant (\( b^2 - 4ac \)):

\[ b^2 - 4ac = (-2)^2 - 4(1)(-4) = 4 + 16 = 20 \]

Now plug all values into the quadratic formula:

\[ x = \frac{-(-2) \pm \sqrt{20}}{2(1)} = \frac{2 \pm \sqrt{20}}{2} \]

Simplifying \( \sqrt{20} \):

\[ \sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5} \]

Now substitute back into the equation:

\[ x = \frac{2 \pm 2\sqrt{5}}{2} \]

This simplifies to:

\[ x = 1 \pm \sqrt{5} \]

So the solutions to the equation \( x^2 - 2x - 4 = 0 \) are:

\[ x = 1 + \sqrt{5} \quad \text{and} \quad x = 1 - \sqrt{5} \]