a)
[tex]-12x^2+x=0 \ \ |\cdot(-1)\\\\12x^2-x=0\\\\x(12x-1)=0\\\\x=0 \ \vee \ 12x-1=0\\\\x=0 \ \vee \ x=\frac{1}{12}[/tex]
b)
[tex]3x^2-3=0 \ \ |:3\\\\x^2-1=0\\\\(x+1)(x-1)=0\\\\x+1=0 \ \vee \ x-1=0\\\\x=-1 \ \vee \ x=1[/tex]
c)
[tex](2x-5)^2-25=0\\\\4x^2-20x+25-25=0\\\\4x^2-20x=0 \ \ |:4\\\\x^2-5x=0\\\\x(x-5)=0\\\\x=0 \ \vee \ x-5=0\\\\x=0 \ \vee \ x=5[/tex]
d)
[tex]3x^2-15x=-18\\\\3x^2-15x+18=0 \ \ |:3\\\\x^2-5x+6=0\\\\a=1, \ b=-5, \ c=6\\\\\Delta=b^2-4ac\rightarrow(-5)^2-4\cdot1\cdot6=25-24=1\\\\\sqrt{\Delta}=\sqrt1=1\\\\x_1=\frac{-b-\sqrt{\Delta}}{2a}\rightarrow\frac{-(-5)-1}{2\cdot1}=\frac{4}{2}=2\\\\x_2=\frac{-b+\sqrt{\Delta}}{2a}\rightarrow\frac{-(-5)+1}{2\cdot1}=\frac{6}{2}=3[/tex]
