1)
[tex]12x^2-11x+2=0\\\\a=12, \ b=-11, \ c=2\\\\\Delta=(-11)^2-4\cdot12\cdot2=121-96=25\\\\\sqrt{\Delta}=\sqrt{25}=5\\\\x_1=\frac{-(-11)-5}{2\cdot12}=\frac{6}{24}=\frac{1}{4}\\\\x_2=\frac{-(-11)+5}{2\cdot12}=\frac{16}{24}=\frac{2}{3}[/tex]
2)
[tex]-x^2+6x-5=0 \ \ |\cdot(-1)\\\\x^2-6x+5=0\\\\a=1, \ b=-6, \ c=5\\\\\Delta=(-6)^2-4\cdot1\cdot5=36-20=16\\\\\sqrt{\Delta}=\sqrt{16}=4\\\\x_1=\frac{-(-6)-4}{2\cdot1}=\frac{2}{2}=1\\\\x_2=\frac{-(-6)+4}{2\cdot1}=\frac{10}{2}=5[/tex]
3)
[tex]-3x^2+12=0 \ \ |:(-3)\\\\x^2-4=0\\\\(x+2)(x-2)=0\\\\x_1=-2 \ \vee \ x_2=2[/tex]
4)
[tex]5x^2-10x=0 \ \ |:5\\\\x^2-2x=0\\\\x(x-2)=0\\\\x_1=0 \ \vee \ x_2=2[/tex]
