\(x^2-5x-24=0\\\\-5x=3x-8x\\-24=3\cdot(-8)\\\\x^2-5x-24=0\\\\\Downarrow\\\\(x+3)(x-8)=0\iff x+3=0\ \vee\ x-8=0\\\\x=-3\ \vee\ x=8\)
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\(3x^2+x-4=0\\\\a=3;\ b=1;\ c=-4\\\\\Delta=b^2-4ac\to\Delta=1^2-4\cdot3\cdot(-4)=1+48=49\\\\x_1=\frac{-b-\sqrt\Delta}{2a}\to x_1=\frac{-1-\sqrt{49}}{2\cdot3}=\frac{-1-7}{6}=\frac{-8}{6}=-\frac{4}{3}\\\\x_2=\frac{-b+\sqrt\Delta}{2a}\to x_2=\frac{-1+\sqrt{49}}{2\cdot3}=\frac{-1+7}{6}=\frac{6}{6}=1\)
