We have : 

\(\dfrac{x-91}{37}+\dfrac{x-86}{42}+\dfrac{x-78}{50}+\dfrac{x-49}{79}=4\)

\(\Rightarrow\left(\dfrac{x-91}{37}-1\right)+\left(\dfrac{x-86}{42}-1\right)+\left(\dfrac{x-78}{50}-1\right)+\left(\dfrac{x-49}{79}-1\right)=0\)

\(\Rightarrow\dfrac{x-128}{37}+\dfrac{x-128}{42}+\dfrac{x-128}{50}+\dfrac{x-128}{79}=0\)

\(\Rightarrow\left(x-128\right)\left(\dfrac{1}{37}+\dfrac{1}{42}+\dfrac{1}{50}+\dfrac{1}{79}\right)=0\)

But \(\dfrac{1}{37}+\dfrac{1}{42}+\dfrac{1}{50}+\dfrac{1}{79}\ne0\)

\(\Rightarrow x-128=0\)

\(\Rightarrow x=128\)

So the value of x is : \(128\)

Different way:

\(\dfrac{x-91}{37}+\dfrac{x-86}{42}+\dfrac{x-78}{50}+\dfrac{x-49}{79}=4\)

\(=\dfrac{82950}{\left(x-91\right)}+\dfrac{73075}{\left(x-86\right)}+\dfrac{61383}{\left(x-78\right)}+\dfrac{38850}{\left(x-49\right)}=12276600\)

\(=256258x-20524424=1276600\)

\(=256258x=32801024\)

=> x = 128

So: x = 128