[tex]A.\\\\4x^2-x-5=0\quad\implies\quad a=4\,,\ b=-1\,,\ c=-5\\\\\Delta=(-1)^2-4\cdot4\cdot(-5)=81\quad\implies\quad\sqrt\Delta=\sqrt{81}=9\\\\ x_1=\frac{1+9}{2\cdot4}=\frac{10}{8}=1\frac14\ ,\qquad x_2=\frac{1-9}{8}=\frac{-8}{8}=-1\\\\\\B.\\\\-x^2+6x+1=0\quad\implies\quad a=-1\,,\ b=6\,,\ c=1\\\\\Delta=6^2-4\cdot(-1)\cdot1=40\quad\implies\quad\sqrt\Delta=\sqrt{40}=2\sqrt{10}\\\\ x_1=\frac{-6+2\sqrt{10}}{2\cdot(-1)}=\frac{-2(3-\sqrt{10})}{-2}=3-\sqrt{10}\ ,\qquad x_2=\frac{-6-2\sqrt{10}}{-2}=3+\sqrt{10}[/tex]
[tex]C.\\\\4x^2+4x+1=0\\\\(2x)^2+2\cdot2x+1+1^2=0\\\\(2x+1)^2=0\\\\2x+1=0\\\\ 2x=-1\qquad|:2\\\\x=-\frac12\\\\\\D.\\\\7x-3x^2=0\\\\x(7-3x)=0\\\\x=0\quad\vee\quad 7-3x=0\\\\x=0\quad\vee\quad x=\frac73[/tex]
[tex]E.\\\\36x^2-6x=0\\\\6x(6x-1)=0\\\\6x=0\quad\vee\quad6x-1=0\\\\x=0\quad\ \vee\quad6x=1\quad/:6\\\\x=0\ \quad\vee\quad x=\frac16\\\\\\F.\\\\100x^2-81=0\\\\(10x)^2-9^2=0\\\\(10x+9)(10x-9)=0\\\\10x+9=0\quad\vee\quad 10x-9=0\\\\10x=-9\quad\ \ \ \vee\quad 10x=9\\\\{}\ \ x=-\frac9{10}\qquad\vee\quad x=\frac9{10}[/tex]