x+x+1/6x=16

Solution for x+x+1/6x=16 equation:

x+x+1/6x=16

We move all terms to the left:

x+x+1/6x-(16)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/6x-16=0

We multiply all the terms by the denominator


2x*6x-16*6x+1=0

Wy multiply elements

12x^2-96x+1=0

a = 12; b = -96; c = +1;
Δ = b2-4ac
Δ = -962-4·12·1
Δ = 9168
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:

$\sqrt{\Delta}=\sqrt{9168}=\sqrt{16*573}=\sqrt{16}*\sqrt{573}=4\sqrt{573}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-4\sqrt{573}}{2*12}=\frac{96-4\sqrt{573}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+4\sqrt{573}}{2*12}=\frac{96+4\sqrt{573}}{24}
$