The points of intersection can be found by equating the equations of the two parabolas:
2x²-7x+1=8x²+5x+1.
So 6x²+12x=0 (by cancelling the 1s and combining the other like terms).
The common factor is 6x: 6x(x+2)=0, so the x coords of intersection are 0 and -2.
We can work out the y values using either equation: y=1 and 23 respectively.
The points of intersection are (-2,23); (0,1).