From the solution provided from this link: https://www.coursehero.com/tutors-problems/Statistics-and-Probability/43900032--Qn-8-Show-that-if-EY-X-a-bX-then-covX-Y-b-and-a-/

Where were these taken or calculated:

Similarly, we have

E[XY] = E[E[XY|X]] = E[aX + bX^2]

and

Therefore, we have

bE[X^2] - bE[X]E[X] = E[XY] - aE[X]