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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-18x^2)/216x^2+108x/216x^2+144x/216x^2=0

We multiply all the terms by the denominator


(-18x^2)+108x+144x=0

We add all the numbers together, and all the variables

(-18x^2)+252x=0

We get rid of parentheses

-18x^2+252x=0

a = -18; b = 252; c = 0;
Δ = b2-4ac
Δ = 2522-4·(-18)·0
Δ = 63504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{63504}=252$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(252)-252}{2*-18}=\frac{-504}{-36}
=+14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(252)+252}{2*-18}=\frac{0}{-36}
=0
$