X+1/6x+2x=190

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

X+1/6X+2X=190

We move all terms to the left:

X+1/6X+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}
$