Answer
$x = \dfrac{-3 ± \sqrt {41}}{4}$
Work Step by Step
We are asked to solve this quadratic equation using the quadratic formula, which is given as:
$x = \dfrac{-b ± \sqrt {b^2 - 4ac}}{2a}$, where $a$ is the coefficient of the $x^2$ term, $b$ is the coefficient of the $x$ term, and $c$ is the constant term.
Plug in the values $a=2, b=3, c=-4$ into this formula to obtain:
$x = \dfrac{-3 ± \sqrt {3^2 - 4(2)(-4)}}{2(2)}$
$x = \dfrac{-3 ± \sqrt {9 - 4(2)(-4)}}{2(2)}$
$x = \dfrac{-3 ± \sqrt {9 + 32}}{4}$
$x = \dfrac{-3 ± \sqrt {41}}{4}$
