Ok, so like i'm late to the thread but anyway have a look :)
so like y=mx+b but the b is zero since the line goes through the origin.
and... this line touches y = x^2+3x+5 twice it's a little cheeky...
so I equate the y's ;
As such, mx=x^2+3x+5
solve for x , 0 = x^2 +x(3-m) + 5
quadratic...