kalieghmernar
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# using the quadratic formula to solve 7x2 – x = 7, what are the values of x?

$7x^2-x=7\\7x^2-x-7=0\\\\a=7;\ b=-1;\ c=-7\\\Delta=b^2-4ac\\\\\Delta=(-1)^2-4\cdot7\cdot(-7)=1+196=197 \ \textgreater \ 0\\\\therefore\\x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\x_1=\dfrac{1-\sqrt{197}}{2\cdot7}=\boxed{\dfrac{1-\sqrt{197}}{14}}\\\\x_2=\dfrac{1+\sqrt{197}}{2\cdot7}=\boxed{\dfrac{1+\sqrt{197}}{14}}$