2020 AMC 12A Problem 12

Line \ell in the coordinate plane has the equation 3x - 5y + 40 = 0. This line is rotated 45^{\circ} counterclockwise about the point (20, 20) to obtain line k. What is the x-coordinate of the x-intercept of line k?

\textbf{(A) } 10 \qquad \textbf{(B) } 15 \qquad \textbf{(C) } 20 \qquad \textbf{(D) } 25 \qquad \textbf{(E) } 30

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.