Question

find all solutions from the range 0 to 2 pie. tan^2x + tanx -12=0

Answer 1

tan^2 x+tanx-12=0 → tanx=(-1±√(1+48))/2=(-1±7)/2 → tanx=-4, tanx=3.
tanx=-4→ x=-arctan(4)+πn;
tanx=3→ x=arctan(3)+πn;

There are 4 roots on [0,2π]:
x=π-arctan(4),x=2π-arctan(4),
x=arctan(3),x=arctan(3)+π.