Cách 1:
\(-7x^2+2x+5=0\\ \Leftrightarrow-7x^2+7x-5x+5=0\\ \Leftrightarrow-7x\left(x-1\right)-5\left(x-1\right)=0\\ \Leftrightarrow\left(x-1\right)\left(-7x-5\right)\\ \Leftrightarrow\left[{}\begin{matrix}x-1=0\\-7x-5=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{5}{7}\end{matrix}\right.\)
Cách 2:
\(-7x^2+2x+5=0\\ \Leftrightarrow7x^2-2x-5=0\\ \Leftrightarrow\left(\sqrt{7}x\right)^2-2.\sqrt{7}x.\dfrac{1}{\sqrt{7}}+\left(\dfrac{1}{\sqrt{7}}\right)^2-\dfrac{36}{7}=0\\ \Leftrightarrow\left(\sqrt{7}x-\dfrac{1}{\sqrt{7}}\right)^2=\dfrac{36}{7}\\ \Leftrightarrow\left[{}\begin{matrix}\sqrt{7}x-\dfrac{1}{\sqrt{7}}=\dfrac{6\sqrt{7}}{7}\\\sqrt{7}x-\dfrac{1}{\sqrt{7}}=-\dfrac{6\sqrt{7}}{7}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}\sqrt{7}x=\sqrt{7}\\\sqrt{7}x=-\dfrac{5\sqrt{7}}{7}\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{5}{7}\end{matrix}\right.\)
Cách 3:
\(\Delta=b^2-4ac=2^2-4.\left(-7\right).5=144>0\)
=> Pt có 2 ngiệm phân biệt
\(x_1=\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{-2-\sqrt{144}}{2.\left(-7\right)}=1\\ x_2=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{-2+\sqrt{144}}{2.\left(-7\right)}=\dfrac{5}{7}\)
