3x/6x+1/x=1

Solution for 3x/6x+1/x=1 equation:

3x/6x+1/x=1

We move all terms to the left:

3x/6x+1/x-(1)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


3x^2/6x^2+6x/6x^2-1=0

We multiply all the terms by the denominator


3x^2+6x-1*6x^2=0

Wy multiply elements

3x^2-6x^2+6x=0

We add all the numbers together, and all the variables

-3x^2+6x=0

a = -3; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-3)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-3}=\frac{-12}{-6}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-3}=\frac{0}{-6}
=0
$