Question

using the quadratic formula to solve $4x^2 - 3x + 9 = 2x + 1$, what are the values of $x$?\
$\frac{1\pm \sqrt{159}i}{8}$\
$\frac{5\pm \sqrt{153}i}{8}$\
$\frac{5\pm \sqrt{103}i}{8}$\
$\frac{1\pm \sqrt{153}}{8}$

Explanation:

Step1: Rearrange to standard quadratic form

Bring all terms to left side:
$$4x^2 - 3x + 9 - 2x - 1 = 0$$
Simplify:
$$4x^2 - 5x + 8 = 0$$

Step2: Identify a, b, c values

For $ax^2+bx+c=0$, we get:
$a=4$, $b=-5$, $c=8$

Step3: Compute discriminant

Calculate $b^2-4ac$:
$$(-5)^2 - 4(4)(8) = 25 - 128 = -103$$

Step4: Apply quadratic formula

Use $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$:
$$x=\frac{-(-5)\pm\sqrt{-103}}{2(4)}=\frac{5\pm\sqrt{103}i}{8}$$

Answer:

$\boldsymbol{\frac{5\pm\sqrt{103}i}{8}}$ (the third option)