Question

Giải phương trình \(3x^2-7x-4=0\)

Answer 1

`3x^2-7x-4=0`

`<=>3(x^2-7/3x-4/3)=0`

`<=>x^2-2x. 7/6+49/36-97/36=0`

`<=>(x-7/6)^2=97/36`

`<=>|x-7/6|=\sqrt{97}/6`

`<=>x=[7+-\sqrt{97}]/6`

Answer 2

\(3x^2-7x-4=0\)

\(\Leftrightarrow3x^2-3x+4x-4=0\)

\(\Leftrightarrow\left(3x^2-3x\right)+\left(4x-4\right)=0\)

\(\Leftrightarrow3x\left(x-1\right)+4\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(3x+4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\3x+4=0\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{4}{3}\end{matrix}\right.\)