we know that
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]7x^{2}=9+x[/tex]
Equate the equation to zero
[tex]7x^{2}-x-9=0[/tex]
so
[tex]a=7\\b=-1\\c=-9[/tex]
substitute in the formula
[tex]x=\frac{-(-1)(+/-)\sqrt{(-1)^{2}-4(7)(-9)}} {2(7)}[/tex]
[tex]x=\frac{1(+/-)\sqrt{1+252}} {14}[/tex]
[tex]x=\frac{1(+/-)\sqrt{253}}{14}[/tex]
therefore
the answer is
[tex]x=\frac{1(+/-)\sqrt{253}}{14}[/tex]
