Answer
$(1-\sqrt 7,1+\sqrt 7)$
Work Step by Step
Step 1. Graph $f(x)=-x^2+2x+6$ as shown in the figure.
Step 2. The solutions to $f(x)=0$ can be found using the quadratic formula as $x=1\pm\sqrt 7$
Step 3. The interval for $f(x)\gt0$ can be identified from the graph as $(1-\sqrt 7,1+\sqrt 7)$
