Infinite Fractions - 2

$28+\dfrac{2013}{\color{#D61F06}{x}}=\color{#D61F06}{x}$ $\Rightarrow x^2-28x-2013=0$ $\Rightarrow (x+33)(x-61)=0$ $\Rightarrow \Large x=61~~\small{(\because x>0)}$

Let $\color{#D61F06}{x}$ equal to the given expression.

$\Rightarrow 28+\frac { 2013 }{ 28+\frac { 2013 }{ 28+\frac { 2013 }{ 28+\frac { 2013 }{ 28+\dots } } } }=\color{#D61F06}{x}$

$\color{#D61F06}{x}=28+\frac{2013}{\color{#D61F06}{x}}$

$\color{#D61F06}{x}^2-28\color{#D61F06}{x}-2013=0$

By the Quadratic formula ,

$\color{#D61F06}{x}=61,-33$

Because given expression consist only positive terms.Hence, neglecting $-33.$

$\Rightarrow 28+\frac { 2013 }{ 28+\frac { 2013 }{ 28+\frac { 2013 }{ 28+\frac { 2013 }{ 28+\dots } } } } =\color{#D61F06}{61}$