What is the distance between the intersections of the parabolas of y equals 4x squared -12x -3 and y equals x squared plus 11x plus 5 showing key stages of work rounded off to 3 decimal places?

1 If: y = 4x2-12x-3 and y = x2+11x+5

2 Then: 4x2-12x-3 = x2+11x+5

3 And so: 3x2-23x-8 = 0

4 Using the quadratic equation formula: x = -1/3 or x = 8

5 By substitution they intersect at: (-1/3, 13/9) and (8, 157)

6 Length: square root of (-1/3-8)2+(13/9-157)2 = 155.7786099

7 Distance between intersections: 155.779 rounded to 3 decimal places