a) \(2\left(x-1\right)-3x\left(x-5\right)=21\Leftrightarrow2x-2-3x^2+15x=21\)
\(\Leftrightarrow21-2x+2+3x^2-15x=0\Leftrightarrow3x^2-17x+23=0\)
\(\Delta=\left(-17\right)^2-4.3.23=289-276=13>0\)
\(\Rightarrow\) phương trình có 2 nghiệm phân biệt
\(x_1=\dfrac{17-\sqrt{13}}{6}\) ; \(x_2=\dfrac{17+\sqrt{13}}{6}\)
vậy \(x=\dfrac{17-\sqrt{13}}{6}\) ; \(x=\dfrac{17+\sqrt{13}}{6}\)
b) \(\left(x+3\right)-\left(x-4\right)\left(x+8\right)=1\Leftrightarrow x+3-\left(x^2+8x-4x-32\right)=1\)
\(\Leftrightarrow x+3-x^2-8x+4x+32=1\Leftrightarrow-x^2-3x+35=1\)
\(\Leftrightarrow1+x^2+3x-35=0\Leftrightarrow x^2+3x-34=0\)
\(\Delta=\left(3\right)^2-4.\left(-34\right)=9+136=145>0\)
\(\Rightarrow\) phương trình có 2 nghiệm phân biệt
\(x_1=\dfrac{-3-\sqrt{145}}{2}\) ; \(x_2=\dfrac{-3+\sqrt{145}}{2}\)
vậy \(x=\dfrac{-3-\sqrt{145}}{2}\) ; \(x=\dfrac{-3+\sqrt{145}}{2}\)
