a]
[tex]x^2+2=5x-4\\\\x^2+2-5x+4=0\\\\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}=\frac{-(-5)-1}{2\cdot1}=\frac{4}{2}=2\\\\x_2=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+1}{2\cdot1}=\frac{6}{2}=3[/tex]
b]
[tex](x-3)^2=(2-x)(x+4)\\\\x^2-6x+9=2x+8-x^2-4x\\\\x^2-6x+9-2x-8+x^2+4x=0\\\\2x^2-4x+1=0\\\\a=2, \ b=-4, \ c=1\\\\\Delta=(-4)^2-4\cdot2\cdot1=16-8=8\\\\\sqrt{\Delta}=\sqrt8=2\sqrt2\\\\x_1=\frac{-(-4)-2\sqrt2}{4}=\frac{4-2\sqrt2}{4}=\frac{2-\sqrt2}{2}\\\\x_2=\frac{-(-4)+2\sqrt2}{4}=\frac{4+2\sqrt2}{4}=\frac{2+\sqrt2}{2}[/tex]
c]
[tex]x^2+2x=-3x^2\\\\x^2+3x^2+2x=0\\\\4x^2+2x=0 \ \ |:4\\\\x^2+0,5x=0\\\\x(x+0,5)=0\\\\x_1=0 \ \vee \ x=-0,5[/tex]