1/3x+1/6x+1/2=2

Solution for 1/3x+1/6x+1/2=2 equation:

1/3x+1/6x+1/2=2

We move all terms to the left:

1/3x+1/6x+1/2-(2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


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

We calculate fractions


108x^2/72x^2+24x/72x^2+12x/72x^2-2=0

We multiply all the terms by the denominator


108x^2+24x+12x-2*72x^2=0

We add all the numbers together, and all the variables

108x^2+36x-2*72x^2=0

Wy multiply elements

108x^2-144x^2+36x=0

We add all the numbers together, and all the variables

-36x^2+36x=0

a = -36; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-36)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-36}=\frac{-72}{-72}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-36}=\frac{0}{-72}
=0
$