1/6x+x+2x=190

Solution for 1/6x+x+2x=190 equation:

1/6x+x+2x=190

We move all terms to the left:

1/6x+x+2x-(190)=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-190=0

We multiply all the terms by the denominator


3x*6x-190*6x+1=0

Wy multiply elements

18x^2-1140x+1=0

a = 18; b = -1140; c = +1;
Δ = b2-4ac
Δ = -11402-4·18·1
Δ = 1299528
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:

$\sqrt{\Delta}=\sqrt{1299528}=\sqrt{36*36098}=\sqrt{36}*\sqrt{36098}=6\sqrt{36098}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1140)-6\sqrt{36098}}{2*18}=\frac{1140-6\sqrt{36098}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1140)+6\sqrt{36098}}{2*18}=\frac{1140+6\sqrt{36098}}{36}
$