Angle of Intersection Between Two Curves

If two curves meet at a point, the angle between the curves is the angle between the tangent vectors to the curves.
The curves  
\[y=x^2-5x-1\]
  and  
\[y=2x^2+x+7\]
  intersect at the solution to  
\[x^2+x+7=x^2-5x-1 \rightarrow x^2+6x+8=0 \rightarrow (x+4)(x+2)=0\]
.
The curves meet at  
\[x+4=0 \rightarrow x=-4, \; x+2=0 \rightarrow x=-2\]
.
The gradients functions of the curves at this point are  
\[\frac{dy}{dx}=2x-5, \; \frac{dy}{dx}=4x-1\]
  and the gradients at  
\[x=-2\]
  are  
\[2 \times -2-5=-9\]
  and  
\[4 \times -2+1=-7\]
.
The angle between the curves at  
\[x=-2\]
  is  
\[tan^{-1}(-7)-tan^{-1}(-7)=1,79^o\]
.