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 \[tan^{-1}(-7)-tan^{-1}(-7)=1,79^o\]
.