$\dfrac{55-2x}{45}+\dfrac{53-2x}{47}+\dfrac{51-2x}{49}+\dfrac{49-2x}{51}+4=0$
$\to (\dfrac{55-2x}{45}+1)+(\dfrac{53-2x}{47}+1)+(\dfrac{51-2x}{49}+1)+(\dfrac{49-2x}{51}+1)=0$
$\to \dfrac{55-2x+45}{45}+\dfrac{53-2x+47}{47}+\dfrac{51-2x+49}{49}+\dfrac{49-2x+51}{51}=0$
$\to \dfrac{100-2x}{45}+\dfrac{100-2x}{47}+\dfrac{100-2x}{49}+\dfrac{100-2x}{51}=0$
$\to (100-2x)(\dfrac{1}{45}+\dfrac{1}{47}+\dfrac{1}{49}+\dfrac{1}{51})=0$
$\text{Do:}$
$\dfrac{1}{45}+\dfrac{1}{47}+\dfrac{1}{49}+\dfrac{1}{51}\ne0$
$\to 100-2x=0$
$\to x= 50$
