Odpowiedź:
[tex]x^2-x-6=0\\\\a=1\ \ ,\ \ b=-1\ \ ,\ \ c=-6\\\\\Delta=b^2-4ac\\\\\Delta=(-1)^2-4\cdot1\cdot(-6)=1+24=25\\\\\sqrt{\Delta}=\sqrt{25}=5\\\\\\x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2\cdot1}=\frac{1-5}{2}=\frac{-4}{2}=-2\\\\x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2\cdot1}=\frac{1+5}{2}=\frac{6}{2}=3[/tex]
[tex]3x^2+4x+1=0\\\\a=3\ \ ,\ \ b=4\ \ ,\ \ c=1\\\\\Delta=b^2-4ac\\\\\Delta=4^2-4\cdot3\cdot1=16-12=4\\\\\sqrt{\Delta}=\sqrt{4}=2\\\\\\x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-4-2}{2\cdot3}=\frac{-6}{6}=-1\\\\x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-4+2}{2\cdot3}=\frac{-2}{6}=-\frac{1}{3}[/tex]
[tex]4x^2-7x-2=0\\\\a=4\ \ ,\ \ b=-7\ \ ,\ \ c=-2\\\\\Delta=b^2-4ac\\\\\Delta=(-7)^2-4\cdot4\cdot(-2)=49+32=81\\\\\sqrt{\Delta}=\sqrt{81}=9\\\\\\x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-9}{2\cdot4}=\frac{7-9}{8}=\frac{-2}{8}=-\frac{1}{4}\\\\x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+9}{2\cdot4}=\frac{7+9}{8}=\frac{16}{8}=2[/tex]
