[tex]a)\\\\x^2- 5x + 4=0\\\\a=1,\ \ b=-5,\ \ c=4\\\\\Delta =b^2-4ac=(-5)^2-4*1*4=25-16=9\\\\\sqrt{\Delta }=\sqrt{9}=3\\\\x_{1}=\frac{-b-\sqrt{\Delta }}{2a}=\frac{5-3}{2*1}=\frac{2}{2}=1\\\\x_{2}=\frac{-b+\sqrt{\Delta }}{2a}=\frac{5+3}{2*1}=\frac{8}{2}= 4[/tex]
[tex]c)\\\\4x^2- x -5=0\\\\a=4,\ \ b=-1,\ \ c=-5\\\\\Delta =b^2-4ac=(-1)^2-4*4*(-5) = 1+80=81\\\\\sqrt{\Delta }=\sqrt{81}=9\\\\x_{1}=\frac{-b-\sqrt{\Delta }}{2a}=\frac{1-9}{2*4}=\frac{-8}{8 }=-1\\\\x_{2}=\frac{-b+\sqrt{\Delta }}{2a}=\frac{1+9}{2*4}=\frac{10}{8 }= \frac{5}{4}=1\frac{1}{4}[/tex]
[tex]d)\\\\6x 2 - 2x - 1 =0\\\\a=6,\ \ b=-2,\ \ c=-1\\\\\Delta =b^2-4ac=(-2)^2-4* 6*(-1) = 4+24=28\\\\\sqrt{\Delta }=\sqrt{28}= \sqrt{4*7}=2\sqrt{7}\\\\x_{1}=\frac{-b-\sqrt{\Delta }}{2a}=\frac{ 2-2\sqrt{7}}{2*6}=\frac{ \not{2}^1(1-\sqrt{7})}{2*6}= \frac{ 1-\sqrt{7}}{ 6} \\\\x_{2}=\frac{-b+\sqrt{\Delta }}{2a}=\frac{ 2+2\sqrt{7}}{2*6}=\frac{ 2(1+\sqrt{7})}{2*6}= \frac{ 1+\sqrt{7}}{ 6}[/tex]
