The equation you've written seems to be intended to represent the sum of an arithmetic series. Specifically, it looks like you're dealing with the series where numbers start from 1 and go up to \( x \), and their sum equals 5050. This is consistent with the formula for the sum of the first \( n \) natural numbers:

\[
S = \frac{n(n + 1)}{2}
\]

Given \( S = 5050 \), we can set up the equation:

\[
\frac{x(x + 1)}{2} = 5050
\]

Multiply both sides by 2 to clear the fraction:

\[
x(x + 1) = 10100
\]

Next, solve the quadratic equation:

\[
x^2 + x - 10100 = 0
\]

Use the quadratic formula to solve for \( x \). The quadratic formula is:

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

For this equation, \( a = 1 \), \( b = 1 \), and \( c = -10100 \). Plug these into the formula:

\[
x = \frac{-1 \pm \sqrt{1^2 - 4 \cdot 1 \cdot (-10100)}}{2 \cdot 1}
\]

\[
x = \frac{-1 \pm \sqrt{1 + 40400}}{2}
\]

\[
x = \frac{-1 \pm \sqrt{40401}}{2}
\]

The value of \(\sqrt{40401}\) is 201. So:

\[
x = \frac{-1 \pm 201}{2}
\]

This gives two solutions:

1. \(\frac{-1 + 201}{2} = \frac{200}{2} = 100\)
2. \(\frac{-1 - 201}{2} = \frac{-202}{2} = -101\) (not a valid solution since \( x \) must be positive)

Thus, the solution is \( x = 100 \). Therefore, the sum of the numbers from 1 to 100 is 5050.