It's extremely messy.  Are you sure you didn't make any
mistakes in copying those three line's equations?

Solve each pair of equations to find the three vertices
of the triangle, which are the messy points as shown.

Then substitute those horrible points in



and you get three equations in the three unknowns
D,E, and F, and you solve that horrible system
of three equations and three unknowns.  After an 
hour's work you find that

D = -785/128, E = -375/64, and F = -105/8

So the equation of the circle is:



It's a terrible answer, but according to what is
given, this is absolutely correct.  However, it 
is hard to believe that any teacher would assign
a problem to a student which would come out so
terrible, when there are many other problems
which come out with whole numbers that would
show exactly the same principle.  Maybe you
copied a sign wrong or something.  Check and see.

Edwin