If Joseph was Jesus's adoptive father then did Jesus really have David's blood? I'm new to this site, but I'm as well searching for answers of several questions I've been facing.

Last Monday, I had a question involving the relationship of Jesus and Joseph.
So far I know, Joseph has been a long-descendant of David. and I believe Jesus was also supposed to have David's blood, because that was the reason why Joseph became his 'mortal father'

But since Maria was pregnant without involving intercourse with Joseph, then Joseph would theoretically have adopted Jesus as his son, breaking the connection of David's blood.

So, to repeat my question again, Is it true that Jesus has the blood from Joseph and finally, also David?
These are two lineages in the Gospels.  One - which you have cited - in Matthew, which traces Jesus' ancestry through Joseph, and another in Luke which traces His ancestry through Mary.  Joseph's genealogy, however, also applies to Mary in that she, like he, was of the house and lineage of David (Luke 2:4).

John Chrysostom addresses your question directly in a 4th century homily on Matthew:


  “But whence is it manifest that He is of David?” one may say. For if
  He was not sprung of a man, but from a woman only, and the Virgin hath
  not her genealogy traced, how shall we know that He was of David’s
  race? Thus, there are two things inquired; both why His mother’s
  genealogy is not recited, and wherefore it can be that Joseph is
  mentioned by them, who hath no part in the birth: since the latter
  seems to be superfluous, and the former a defect.
  
  Of which then is it necessary to speak first? How the Virgin is of
  David. How then shall we know that she is of David? Hearken unto God,
  telling Gabriel to go unto “a virgin betrothed to a man (whose name
  was Joseph), of the house and lineage of David.” What now wouldest
  thou have plainer than this, when thou hast heard that the Virgin was
  of the house and lineage of David?
  
  Hence it is evident that Joseph also was of the same. Yes, for there
  was a law, which bade that it should not be lawful to take a wife from
  any other stock, but from the same tribe. And the patriarch Jacob also
  foretold that He should arise out of the tribe of Judah, saying on
  this wise: there shall not fail a ruler out of Judah, nor a governor
  out of his loins, until He come for whom it is appointed, and He is
  the expectation of the Gentiles.” [Genesis 49:10 LXX]
  
  Homily II on Matthew