(x-2)^2*(x-3)=12(x-3)

[latex] (x-2)^{2}*(x-3)=12(x-3) [/latex] [latex] (x^{2}-4x+4)*(x-3)=12x-36[/latex] [latex] x^{3}-7 x^{2} +16x-12-12x+36=0 [/latex] [latex] x^{3} -7 x^{2} +4x+24=0[/latex] a=-7; b=4; c=24 [latex]Q= \frac{(( -7^{2} )-3*4)}{9} =4 \frac{1}{9} [/latex] [latex]R= \frac{2*(- 7^{3} )-9*(-7)*4+27*24}{54} =3 \frac{26}{27} [/latex] Три действительный корня: [latex]x_1=-1 \frac{58}{125} [/latex] [latex]x_2=5 \frac{58}{125} [/latex] [latex]x_3=3[/latex]