$\left ( \color{#FF6800}{ 24 } \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) \left ( \color{#FF6800}{ 16 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \right ) = 210$
$ $ Organize the expression $ $
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 64 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 384 } = 210$
$2 x ^ { 2 } - 64 x + 384 = \color{#FF6800}{ 210 }$
$ $ Move the expression to the left side and change the symbol $ $
$2 x ^ { 2 } - 64 x + 384 \color{#FF6800}{ - } \color{#FF6800}{ 210 } = 0$
$2 x ^ { 2 } - 64 x + \color{#FF6800}{ 384 } \color{#FF6800}{ - } \color{#FF6800}{ 210 } = 0$
$ $ Subtract $ 210 $ from $ 384$
$2 x ^ { 2 } - 64 x + \color{#FF6800}{ 174 } = 0$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 64 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 174 } = \color{#FF6800}{ 0 }$
$ $ Solve the quadratic equation $ ax^{2}+bx+c=0 $ using the quadratic formula $ \dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 64 } \right ) \pm \sqrt{ \left ( \color{#FF6800}{ - } \color{#FF6800}{ 64 } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 174 } } } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } }$
$x = \dfrac { \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } 64 \right ) \pm \sqrt{ \left ( - 64 \right ) ^ { 2 } - 4 \times 2 \times 174 } } { 2 \times 2 }$
$ $ Simplify Minus $ $
$x = \dfrac { 64 \pm \sqrt{ \left ( - 64 \right ) ^ { 2 } - 4 \times 2 \times 174 } } { 2 \times 2 }$
$x = \dfrac { 64 \pm \sqrt{ \left ( \color{#FF6800}{ - } \color{#FF6800}{ 64 } \right ) ^ { \color{#FF6800}{ 2 } } - 4 \times 2 \times 174 } } { 2 \times 2 }$
$ $ Remove negative signs because negative numbers raised to even powers are positive $ $
$x = \dfrac { 64 \pm \sqrt{ 64 ^ { 2 } - 4 \times 2 \times 174 } } { 2 \times 2 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 64 } \pm \sqrt{ \color{#FF6800}{ 64 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 174 } } } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } }$
$ $ Organize the expression $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 64 } \pm \sqrt{ \color{#FF6800}{ 2704 } } } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } }$
$x = \dfrac { 64 \pm \sqrt{ \color{#FF6800}{ 2704 } } } { 2 \times 2 }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$x = \dfrac { 64 \pm \color{#FF6800}{ 52 } } { 2 \times 2 }$
$x = \dfrac { 64 \pm 52 } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } }$
$ $ Multiply $ 2 $ and $ 2$
$x = \dfrac { 64 \pm 52 } { \color{#FF6800}{ 4 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 64 } \pm \color{#FF6800}{ 52 } } { \color{#FF6800}{ 4 } } }$
$ $ Separate the answer $ $
$\begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 64 } \color{#FF6800}{ + } \color{#FF6800}{ 52 } } { \color{#FF6800}{ 4 } } } \\ \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 64 } \color{#FF6800}{ - } \color{#FF6800}{ 52 } } { \color{#FF6800}{ 4 } } } \end{array}$
$\begin{array} {l} x = \dfrac { \color{#FF6800}{ 64 } \color{#FF6800}{ + } \color{#FF6800}{ 52 } } { 4 } \\ x = \dfrac { 64 - 52 } { 4 } \end{array}$
$ $ Add $ 64 $ and $ 52$
$\begin{array} {l} x = \dfrac { \color{#FF6800}{ 116 } } { 4 } \\ x = \dfrac { 64 - 52 } { 4 } \end{array}$
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 116 } } { \color{#FF6800}{ 4 } } } \\ x = \dfrac { 64 - 52 } { 4 } \end{array}$
$ $ Do the reduction of the fraction format $ $
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 29 } } { \color{#FF6800}{ 1 } } } \\ x = \dfrac { 64 - 52 } { 4 } \end{array}$
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 29 } } { \color{#FF6800}{ 1 } } } \\ x = \dfrac { 64 - 52 } { 4 } \end{array}$
$ $ Reduce the fraction to the lowest term $ $
$\begin{array} {l} x = \color{#FF6800}{ 29 } \\ x = \dfrac { 64 - 52 } { 4 } \end{array}$
$\begin{array} {l} x = 29 \\ x = \dfrac { \color{#FF6800}{ 64 } \color{#FF6800}{ - } \color{#FF6800}{ 52 } } { 4 } \end{array}$
$ $ Subtract $ 52 $ from $ 64$
$\begin{array} {l} x = 29 \\ x = \dfrac { \color{#FF6800}{ 12 } } { 4 } \end{array}$
$\begin{array} {l} x = 29 \\ x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 12 } } { \color{#FF6800}{ 4 } } } \end{array}$
$ $ Do the reduction of the fraction format $ $
$\begin{array} {l} x = 29 \\ x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } } { \color{#FF6800}{ 1 } } } \end{array}$
$\begin{array} {l} x = 29 \\ x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } } { \color{#FF6800}{ 1 } } } \end{array}$
$ $ Reduce the fraction to the lowest term $ $
$\begin{array} {l} x = 29 \\ x = \color{#FF6800}{ 3 } \end{array}$