The range of α, if  (α, α2) lies inside the triangle having sides along the lines 2x+3y=1, x+2y-3=0, 6y=5x-1

Let A, B, C be vertices of the triangle. A=(−7,5), B=54,78C=13,19. Sign of A w.r.t. BC to -ve.If P lies inside the triangle ABC, then sign of P will be the same as sign of A w.r.t. the line BC⇒5α−6α2−1<0.....(i)similarly 2α+3α2−1>0.....(ii)And α+2α2−3<0.....(iii)Solving (i), (ii) and (iii) for  and then taking intersection,we get α∈12,1∪−32,−1