x+1/6x=110

Solution for x+1/6x=110 equation:

x+1/6x=110

We move all terms to the left:

x+1/6x-(110)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


x*6x-110*6x+1=0

Wy multiply elements

6x^2-660x+1=0

a = 6; b = -660; c = +1;
Δ = b2-4ac
Δ = -6602-4·6·1
Δ = 435576
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:

$\sqrt{\Delta}=\sqrt{435576}=\sqrt{4*108894}=\sqrt{4}*\sqrt{108894}=2\sqrt{108894}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-660)-2\sqrt{108894}}{2*6}=\frac{660-2\sqrt{108894}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-660)+2\sqrt{108894}}{2*6}=\frac{660+2\sqrt{108894}}{12}
$