It seems like there was a formatting issue, but I understand you are asking about the quadratic equation \(x^2 + 4x - 22 = 0\).

To solve this quadratic equation, we can use the quadratic formula:
\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a} \]

For the equation \(x^2 + 4x - 22 = 0\), the coefficients are:
- \(a = 1\)
- \(b = 4\)
- \(c = -22\)

Substituting these into the quadratic formula gives:
\[ x = \frac{{-4 \pm \sqrt{{4^2 - 4 \cdot 1 \cdot (-22)}}}}{2 \cdot 1} \]
\[ x = \frac{{-4 \pm \sqrt}}{2} \]
\[ x = \frac{{-4 \pm \sqrt}}{2} \]

The square root of 104 can be simplified:
\[ \sqrt{104} = \sqrt{4 \times 26} = 2\sqrt{26} \]

So the expression becomes:
\[ x = \frac{{-4 \pm 2\sqrt{26}}}{2} \]

Simplifying further:
\[ x = -2 \pm \sqrt{26} \]

Thus, the solutions to the equation \(x^2 + 4x - 22 = 0\) are:
\[ x = -2 + \sqrt{26} \]
or
\[ x = -2 - \sqrt{26} \]