x+x+(1/6x)=13

Solution for x+x+(1/6x)=13 equation:

x+x+(1/6x)=13

We move all terms to the left:

x+x+(1/6x)-(13)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+x+(+1/6x)-13=0

We add all the numbers together, and all the variables

2x+(+1/6x)-13=0

We get rid of parentheses

2x+1/6x-13=0

We multiply all the terms by the denominator


2x*6x-13*6x+1=0

Wy multiply elements

12x^2-78x+1=0

a = 12; b = -78; c = +1;
Δ = b2-4ac
Δ = -782-4·12·1
Δ = 6036
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:

$\sqrt{\Delta}=\sqrt{6036}=\sqrt{4*1509}=\sqrt{4}*\sqrt{1509}=2\sqrt{1509}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1509}}{2*12}=\frac{78-2\sqrt{1509}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1509}}{2*12}=\frac{78+2\sqrt{1509}}{24}
$