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$$2 x ^ { 2 } - 5 x - 3 = 0$$
$\begin{array} {l} x = 3 \\ x = - \dfrac { 1 } { 2 } \end{array}$
$x = \dfrac { \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } 5 \right ) \pm \sqrt{ \left ( - 5 \right ) ^ { 2 } - 4 \times 2 \times \left ( - 3 \right ) } } { 2 \times 2 }$
 Simplify Minus 
$x = \dfrac { 5 \pm \sqrt{ \left ( - 5 \right ) ^ { 2 } - 4 \times 2 \times \left ( - 3 \right ) } } { 2 \times 2 }$
$x = \dfrac { 5 \pm \sqrt{ \left ( \color{#FF6800}{ - } \color{#FF6800}{ 5 } \right ) ^ { \color{#FF6800}{ 2 } } - 4 \times 2 \times \left ( - 3 \right ) } } { 2 \times 2 }$
 Remove negative signs because negative numbers raised to even powers are positive 
$x = \dfrac { 5 \pm \sqrt{ 5 ^ { 2 } - 4 \times 2 \times \left ( - 3 \right ) } } { 2 \times 2 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 5 \pm \sqrt{ 5 ^ { 2 } - 4 \times 2 \times \left ( - 3 \right ) } } { 2 \times 2 } }$
 Organize the expression 
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 5 \pm \sqrt{ 49 } } { 2 \times 2 } }$
$x = \dfrac { 5 \pm \sqrt{ \color{#FF6800}{ 49 } } } { 2 \times 2 }$
 Organize the part that can be taken out of the radical sign inside the square root symbol 
$x = \dfrac { 5 \pm \color{#FF6800}{ 7 } } { 2 \times 2 }$
$x = \dfrac { 5 \pm 7 } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } }$
 Multiply $2$ and $2$
$x = \dfrac { 5 \pm 7 } { \color{#FF6800}{ 4 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 5 \pm 7 } { 4 } }$
 Separate the answer 
$\begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 5 + 7 } { 4 } } \\ \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 5 - 7 } { 4 } } \end{array}$
$\begin{array} {l} x = \dfrac { \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 7 } } { 4 } \\ x = \dfrac { 5 - 7 } { 4 } \end{array}$
 Add $5$ and $7$
$\begin{array} {l} x = \dfrac { \color{#FF6800}{ 12 } } { 4 } \\ x = \dfrac { 5 - 7 } { 4 } \end{array}$
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { 12 } { 4 } } \\ x = \dfrac { 5 - 7 } { 4 } \end{array}$
 Do the reduction of the fraction format 
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { 3 } { 1 } } \\ x = \dfrac { 5 - 7 } { 4 } \end{array}$
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { 3 } { 1 } } \\ x = \dfrac { 5 - 7 } { 4 } \end{array}$
 Reduce the fraction to the lowest term 
$\begin{array} {l} x = \color{#FF6800}{ 3 } \\ x = \dfrac { 5 - 7 } { 4 } \end{array}$
$\begin{array} {l} x = 3 \\ x = \dfrac { \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 7 } } { 4 } \end{array}$
 Subtract $7$ from $5$
$\begin{array} {l} x = 3 \\ x = \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 2 } } { 4 } \end{array}$
$\begin{array} {l} x = 3 \\ x = \color{#FF6800}{ \dfrac { - 2 } { 4 } } \end{array}$
 Do the reduction of the fraction format 
$\begin{array} {l} x = 3 \\ x = \color{#FF6800}{ \dfrac { - 1 } { 2 } } \end{array}$
$\begin{array} {l} x = 3 \\ x = \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 1 } } { 2 } \end{array}$
 Move the minus sign to the front of the fraction 
$\begin{array} {l} x = 3 \\ x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 2 } } \end{array}$
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