Answer
$x = \frac{3±\sqrt{23}i}{4}$
Work Step by Step
$x(2x - 3) = -4$
Simplify.
$2x^2 - 3x = -4$
Add $4$ to both sides.
$2x^2 - 3x+4 = -4+4$
$2x^2 - 3x+4 = 0$
Use the quadratic formula: $x = \frac{-b±\sqrt{b^2-4ac}}{2a}$
$a=2$, $b=-3$, $c=4$
$x = \frac{-(-3)±\sqrt{(-3)^2-(4⋅2⋅4)}}{(2⋅2)}$
$x = \frac{3±\sqrt{9-32}}{4}$
$x = \frac{3±\sqrt{-23}}{4}$
$x = \frac{3±\sqrt{23}i}{4}$
