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$$4 x ^ { 2 } - 9 = 0$$
$\begin{array} {l} x = \dfrac { 3 } { 2 } \\ x = - \dfrac { 3 } { 2 } \end{array}$
$x = \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 0 } \pm \sqrt{ 0 ^ { 2 } - 4 \times 4 \times \left ( - 9 \right ) } } { 2 \times 4 }$
 0 has no sign 
$x = \dfrac { \color{#FF6800}{ 0 } \pm \sqrt{ 0 ^ { 2 } - 4 \times 4 \times \left ( - 9 \right ) } } { 2 \times 4 }$
$x = \dfrac { 0 \pm \sqrt{ \color{#FF6800}{ 0 } ^ { \color{#FF6800}{ 2 } } - 4 \times 4 \times \left ( - 9 \right ) } } { 2 \times 4 }$
 The power of 0 is 0 
$x = \dfrac { 0 \pm \sqrt{ \color{#FF6800}{ 0 } - 4 \times 4 \times \left ( - 9 \right ) } } { 2 \times 4 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 0 \pm \sqrt{ 0 - 4 \times 4 \times \left ( - 9 \right ) } } { 2 \times 4 } }$
 Organize the expression 
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 0 \pm \sqrt{ 144 } } { 2 \times 4 } }$
$x = \dfrac { 0 \pm \sqrt{ \color{#FF6800}{ 144 } } } { 2 \times 4 }$
 Organize the part that can be taken out of the radical sign inside the square root symbol 
$x = \dfrac { 0 \pm \color{#FF6800}{ 12 } } { 2 \times 4 }$
$x = \dfrac { 0 \pm 12 } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } }$
 Multiply $2$ and $4$
$x = \dfrac { 0 \pm 12 } { \color{#FF6800}{ 8 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 0 \pm 12 } { 8 } }$
 Separate the answer 
$\begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 0 + 12 } { 8 } } \\ \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 0 - 12 } { 8 } } \end{array}$
$\begin{array} {l} x = \dfrac { \color{#FF6800}{ 0 } + 12 } { 8 } \\ x = \dfrac { 0 - 12 } { 8 } \end{array}$
 0 does not change when you add or subtract 
$\begin{array} {l} x = \dfrac { 12 } { 8 } \\ x = \dfrac { 0 - 12 } { 8 } \end{array}$
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { 12 } { 8 } } \\ x = \dfrac { 0 - 12 } { 8 } \end{array}$
 Do the reduction of the fraction format 
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { 3 } { 2 } } \\ x = \dfrac { 0 - 12 } { 8 } \end{array}$
$\begin{array} {l} x = \dfrac { 3 } { 2 } \\ x = \dfrac { \color{#FF6800}{ 0 } - 12 } { 8 } \end{array}$
 0 does not change when you add or subtract 
$\begin{array} {l} x = \dfrac { 3 } { 2 } \\ x = \dfrac { - 12 } { 8 } \end{array}$
$\begin{array} {l} x = \dfrac { 3 } { 2 } \\ x = \color{#FF6800}{ \dfrac { - 12 } { 8 } } \end{array}$
 Do the reduction of the fraction format 
$\begin{array} {l} x = \dfrac { 3 } { 2 } \\ x = \color{#FF6800}{ \dfrac { - 3 } { 2 } } \end{array}$
$\begin{array} {l} x = \dfrac { 3 } { 2 } \\ x = \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 3 } } { 2 } \end{array}$
 Move the minus sign to the front of the fraction 
$\begin{array} {l} x = \dfrac { 3 } { 2 } \\ x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 2 } } \end{array}$
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