Question

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Answer 1

The quadratic formula is 
$x= \dfrac{-b\pm \sqrt{b^2-4ac} }{2a}$.

For the equation $4x^2-3x+9=2x+1$, we must first convert it into standard form $ax^2+bx+c=0$. We see it is $4x^2-5x+8=0$. From this, our coefficients are $a=4, b=-5$ and $c=8$. 

We plug these coefficients into the quadratic formula.

$x= \dfrac{-(-5)\pm\sqrt{(-5)^2-4(4)(8)} }{2(4)} \\ \\ \\ \\ x = \dfrac{5\pm\sqrt{-103}}{8} \\ \\ \\ \\ x = \dfrac{5\pm\ i\sqrt{103}}{8}$

The answer is C.