[tex](a)\;(4x+3)(3x-7)=0\\12x^2-28x+9x-21=0\\12x^2-19x-21=0\\\\a=12,\;b=-19,\;c=-21\\\\\Delta=b^2-4ac\\\Delta=(-19)^2-4\cdot12\cdot(-21)\\\Delta=361+1008\\\Delta=1369\\\\x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\x=\dfrac{-(-19)\pm\sqrt{1369}}{2\cdot12}\\\\x=\dfrac{19\pm37}{24}\\\\x_1=\dfrac{19+37}{24}=\dfrac{56}{24}=\dfrac{7}{3}\\\\x_22=\dfrac{19-37}{24}=\dfrac{-18}{24}=-\dfrac{3}{4}\\\\\\\\(b)\;(2x-1)(3x-2)=0\\6x^2-4x-3x+2=0\\6x^2-7x+2=0\\\\a=6,\;b=-7,\;c=2\\\\\Delta=b^2-4ac\\\Delta=(-7)^2-4\cdot6\cdot2\\\Delta=49-48\\\Delta=1\\\\x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\x=\dfrac{-(-7)\pm\sqrt{1}}{2\cdot6}\\\\x=\dfrac{7\pm1}{12}\\\\x_1=\dfrac{7+1}{12}=\dfrac{8}{12}=\dfrac{2}{3}\\\\x_2=\dfrac{7-1}{12}=\dfrac{6}{12}=\dfrac{1}{2}[/tex]
