a)
[tex](3x-5)(x+2)\geq (5x-6)(x+2)\\3x^2+6x-5x-10\geq 5x^2+10x-6x-12\\3x^2+6x-5x-10- 5x^2-10x+6x+12\geq 0\\-2x^2-3x+2\geq 0\\\Delta=(-3)^2-4*(-2)*2=9+16=25\\\sqrt\Delta=5\\x_1=\frac{3-5}{2*(-2)}=\frac{-2}{-4}=\frac{1}{2}\\x_2=\frac{3+5}{2*(-2)}=\frac{8}{-4}=-2\\x\in\left < -2,\frac{1}{2}\right >[/tex]
b)
[tex](4x-2)^2 < (3x-8)^2\\16x^2-16x+4 < 9x^2-48x+64\\16x^2-16x+4-9x^2+48x-64 < 0\\7x^2+32x-60 < 0\\\Delta=32^2-4*7*(-60)=1024+1680=2704\\\sqrt\Delta=52\\x_1=\frac{-32-52}{2*7}=\frac{-84}{14}=-6\\x_2=\frac{-32+52}{2*7}=\frac{20}{14}=1\frac{3}{7}\\x\in(-6,1\frac{3}{7})[/tex]
