1/6x+1=x

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

1/6x+1=x

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+1/6x+1=0

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2+6x+1=0

a = -6; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·(-6)·1
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{15}}{2*-6}=\frac{-6-2\sqrt{15}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{15}}{2*-6}=\frac{-6+2\sqrt{15}}{-12}
$