x+5/6x=55

Solution for x+5/6x=55 equation:

x+5/6x=55

We move all terms to the left:

x+5/6x-(55)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


x*6x-55*6x+5=0

Wy multiply elements

6x^2-330x+5=0

a = 6; b = -330; c = +5;
Δ = b2-4ac
Δ = -3302-4·6·5
Δ = 108780
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108780}=\sqrt{196*555}=\sqrt{196}*\sqrt{555}=14\sqrt{555}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-330)-14\sqrt{555}}{2*6}=\frac{330-14\sqrt{555}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-330)+14\sqrt{555}}{2*6}=\frac{330+14\sqrt{555}}{12}
$