$\begin{array} {l} x = \dfrac { - 2 + \sqrt{ 2 } i } { 2 } \\ x = \dfrac { - 2 - \sqrt{ 2 } i } { 2 } \end{array}$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 3 } = \color{#FF6800}{ 0 }$
$ $ Solve the quadratic equation $ ax^{2}+bx+c=0 $ using the quadratic formula $ \dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { - 4 \pm \sqrt{ 4 ^ { 2 } - 4 \times 2 \times 3 } } { 2 \times 2 } }$
$x = \dfrac { - 4 \pm \sqrt{ \color{#FF6800}{ 4 } ^ { \color{#FF6800}{ 2 } } - 4 \times 2 \times 3 } } { 2 \times 2 }$
$ $ Calculate power $ $
$x = \dfrac { - 4 \pm \sqrt{ \color{#FF6800}{ 16 } - 4 \times 2 \times 3 } } { 2 \times 2 }$
$x = \dfrac { - 4 \pm \sqrt{ 16 \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } } } { 2 \times 2 }$
$ $ Multiply the numbers $ $
$x = \dfrac { - 4 \pm \sqrt{ 16 \color{#FF6800}{ - } \color{#FF6800}{ 24 } } } { 2 \times 2 }$
$x = \dfrac { - 4 \pm \sqrt{ \color{#FF6800}{ 16 } \color{#FF6800}{ - } \color{#FF6800}{ 24 } } } { 2 \times 2 }$
$ $ Subtract $ 24 $ from $ 16$
$x = \dfrac { - 4 \pm \sqrt{ \color{#FF6800}{ - } \color{#FF6800}{ 8 } } } { 2 \times 2 }$
$x = \dfrac { - 4 \pm \sqrt{ \color{#FF6800}{ - } \color{#FF6800}{ 8 } } } { 2 \times 2 }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$x = \dfrac { - 4 \pm \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 2 } } \color{#FF6800}{ i } } { 2 \times 2 }$
$x = \dfrac { - 4 \pm 2 \sqrt{ 2 } i } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } }$
$ $ Multiply $ 2 $ and $ 2$
$x = \dfrac { - 4 \pm 2 \sqrt{ 2 } i } { \color{#FF6800}{ 4 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { - 4 \pm 2 \sqrt{ 2 } i } { 4 } }$
$ $ Separate the answer $ $
$\begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { - 4 + 2 \sqrt{ 2 } i } { 4 } } \\ \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { - 4 - 2 \sqrt{ 2 } i } { 4 } } \end{array}$
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { - 4 + 2 \sqrt{ 2 } i } { 4 } } \\ x = \dfrac { - 4 - 2 \sqrt{ 2 } i } { 4 } \end{array}$
$ $ Reduce the fraction $ $
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { - 2 + \sqrt{ 2 } i } { 2 } } \\ x = \dfrac { - 4 - 2 \sqrt{ 2 } i } { 4 } \end{array}$
$\begin{array} {l} x = \dfrac { - 2 + \sqrt{ 2 } i } { 2 } \\ x = \color{#FF6800}{ \dfrac { - 4 - 2 \sqrt{ 2 } i } { 4 } } \end{array}$
$ $ Reduce the fraction $ $
$\begin{array} {l} x = \dfrac { - 2 + \sqrt{ 2 } i } { 2 } \\ x = \color{#FF6800}{ \dfrac { - 2 - \sqrt{ 2 } i } { 2 } } \end{array}$