Beowulf's father Ecgtheow was a good friend of Hrothgar's. Long ago, Hrothergar saved Ecgtheow's life. Beowulf comes to repay his father's "debt" to Hrothgar. This is the 'technical' reason he helps Hrothgar. Really though, Beowulf is a true hero. He seeks out a challenge, and Grendel is the ultimate challenge.
Beowulf introduces himself to Hrothgar and explains that he has come to offer his assistance in defeating the monster Grendel that has been terrorizing the Danes. Beowulf also mentions his father's relationship with Hrothgar in the past, highlighting their familial connection.
Beowulf owed Hrothgar a favor because Hrothgar helped Beowulf's father in time of need. Additionally, Beowulf is looking to prove himself as a warrior.
Beowulf owes a family debt to Hrothgar because Hrothgar's father helped settle a feud and make peace with Beowulf's father, Ecgtheow. Beowulf's father was indebted to Hrothgar's father for his assistance, which Beowulf sees as a reason to repay the debt by helping Hrothgar against the monster, Grendel.
Edgetho and Hrothgar are not friends. In the epic poem "Beowulf," Edgetho is Beowulf's father and Hrothgar is the king of the Danes whom Beowulf helps by defeating the monster Grendel. There is no indication of friendship between Edgetho and Hrothgar in the poem.
Beowulf's father took refuge in Hrothgar's land after a messy murder back at home. He eventually married Hrothgar's daughter, and then came baby Beowulf. So long story short Hrothgar is Beowulf's grandfather.
'Beowulf' is the epic story that tells us the tale of hero Beowulf, the strongest and bravest of them all and how he defeats monsters and becomes a king. Among several characters we will also meet Hygelac, his uncle and king of the Geats, the one who opens his kingdom's doors and his heart to Beowulf.
Beowulf and his men travel to Hrothgar's kingdom to kill Grendel.
Beowulf asks Hrothgar to send his armor to Hygelac if he is unsuccessful in defeating Grendel.
It takes Beowulf and his men five days to reach Hrothgar.
Beowulf owed Hrothgar a favor because Hrothgar helped Beowulf's father in time of need. Additionally, Beowulf is looking to prove himself as a warrior.
Once at Hrothgar's throne, Beowulf introduces himself as a hero who can crush water sprites, among other things. Therefore he is equipped to defeat Grendel, if Wyrd (or Fate) will have it so. Hrothgar welcomes Beowulf as the son of Ecgtheow, the man whom Hrothgar had helped in settling a feud with the Wylfingas long ago.