$\color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 24 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 36 } = 0$
$ $ Bind the expressions with the common factor $ 4$
$\color{#FF6800}{ 4 } \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 9 } \right ) = 0$
$\color{#FF6800}{ 4 } \left ( \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 9 } \right ) = \color{#FF6800}{ 0 }$
$ $ Divide both sides by $ 4$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 9 } = \color{#FF6800}{ 0 }$
$x = \dfrac { \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } 6 \right ) \pm \sqrt{ \left ( - 6 \right ) ^ { 2 } - 4 \times 1 \times 9 } } { 2 \times 1 }$
$ $ Simplify Minus $ $
$x = \dfrac { 6 \pm \sqrt{ \left ( - 6 \right ) ^ { 2 } - 4 \times 1 \times 9 } } { 2 \times 1 }$
$x = \dfrac { 6 \pm \sqrt{ \left ( \color{#FF6800}{ - } \color{#FF6800}{ 6 } \right ) ^ { \color{#FF6800}{ 2 } } - 4 \times 1 \times 9 } } { 2 \times 1 }$
$ $ Remove negative signs because negative numbers raised to even powers are positive $ $
$x = \dfrac { 6 \pm \sqrt{ 6 ^ { 2 } - 4 \times 1 \times 9 } } { 2 \times 1 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 6 \pm \sqrt{ 6 ^ { 2 } - 4 \times 1 \times 9 } } { 2 \times 1 } }$
$ $ Organize the expression $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 6 \pm \sqrt{ 0 } } { 2 \times 1 } }$
$x = \dfrac { 6 \pm \sqrt{ \color{#FF6800}{ 0 } } } { 2 \times 1 }$
$n square root $ of 0 is 0 $ $
$x = \dfrac { 6 \pm \color{#FF6800}{ 0 } } { 2 \times 1 }$
$x = \dfrac { 6 \pm 0 } { 2 \color{#FF6800}{ \times } \color{#FF6800}{ 1 } }$
$ $ Multiplying any number by 1 does not change the value $ $
$x = \dfrac { 6 \pm 0 } { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 6 \pm 0 } { 2 } }$
$ $ The value will not be changed even if adding or subtracting 0 $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 6 } { 2 } }$
$x = \color{#FF6800}{ \dfrac { 6 } { 2 } }$
$ $ Do the reduction of the fraction format $ $
$x = \color{#FF6800}{ \dfrac { 3 } { 1 } }$
$x = \color{#FF6800}{ \dfrac { 3 } { 1 } }$
$ $ Reduce the fraction to the lowest term $ $
$x = \color{#FF6800}{ 3 }$