2x+x+1/6x=19

Solution for 2x+x+1/6x=19 equation:

2x+x+1/6x=19

We move all terms to the left:

2x+x+1/6x-(19)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/6x-19=0

We multiply all the terms by the denominator


3x*6x-19*6x+1=0

Wy multiply elements

18x^2-114x+1=0

a = 18; b = -114; c = +1;
Δ = b2-4ac
Δ = -1142-4·18·1
Δ = 12924
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:

$\sqrt{\Delta}=\sqrt{12924}=\sqrt{36*359}=\sqrt{36}*\sqrt{359}=6\sqrt{359}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-6\sqrt{359}}{2*18}=\frac{114-6\sqrt{359}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+6\sqrt{359}}{2*18}=\frac{114+6\sqrt{359}}{36}
$