The quadratic formula is
[tex]x= \dfrac{-b\pm \sqrt{b^2-4ac} }{2a} [/tex].
For the equation [tex]4x^2-3x+9=2x+1[/tex], we must first convert it into standard form [tex]ax^2+bx+c=0[/tex]. We see it is [tex]4x^2-5x+8=0[/tex]. From this, our coefficients are [tex]a=4, b=-5[/tex] and [tex]c=8[/tex].
We plug these coefficients into the quadratic formula.
[tex]x= \dfrac{-(-5)\pm\sqrt{(-5)^2-4(4)(8)} }{2(4)} \\ \\ \\ \\ x = \dfrac{5\pm\sqrt{-103}}{8} \\ \\ \\ \\ x = \dfrac{5\pm\ i\sqrt{103}}{8} [/tex]
The answer is C.
