Решить неравенство: (x-1)(3-2x)>-6

Question

Решить неравенство: (x-1)(3-2x)>-6

Answer 1

(x-1)(3-2x)>-6 <=> 3x-3-2x²+2x>-6 <=> -2x²+5x+3>0 <=> 2x²-5x-3 < 0

2x²-5x-3=0
D=5²+4*2*3 = 25+24 = 49
√D=7

x₁=(5+7)/(2*2)=3
x₂=(5-7)/(2*2)=-1/2

2x²-5x-3 = 2(x-3)(x+1/2)

2(x-3)(x+1/2) <0 <=> x∈(-1/2;3)