2/3x+1/6x=5/42

Solution for 2/3x+1/6x=5/42 equation:

2/3x+1/6x=5/42

We move all terms to the left:

2/3x+1/6x-(5/42)=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


We add all the numbers together, and all the variables

2/3x+1/6x-(+5/42)=0

We get rid of parentheses

2/3x+1/6x-5/42=0

We calculate fractions


(-540x^2)/3024x^2+2016x/3024x^2+504x/3024x^2=0

We multiply all the terms by the denominator


(-540x^2)+2016x+504x=0

We add all the numbers together, and all the variables

(-540x^2)+2520x=0

We get rid of parentheses

-540x^2+2520x=0

a = -540; b = 2520; c = 0;
Δ = b2-4ac
Δ = 25202-4·(-540)·0
Δ = 6350400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6350400}=2520$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2520)-2520}{2*-540}=\frac{-5040}{-1080}
=4+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2520)+2520}{2*-540}=\frac{0}{-1080}
=0
$