1/7x+1/6x+1/7=19/42

Solution for 1/7x+1/6x+1/7=19/42 equation:

1/7x+1/6x+1/7=19/42

We move all terms to the left:

1/7x+1/6x+1/7-(19/42)=0


Domain of the equation: 7x!=0

x!=0/7

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

1/7x+1/6x+1/7-(+19/42)=0

We get rid of parentheses

1/7x+1/6x+1/7-19/42=0

We calculate fractions


(-33516x^2)/86436x^2+1008x/86436x^2+14406x/86436x^2+1008x/86436x^2=0

We multiply all the terms by the denominator


(-33516x^2)+1008x+14406x+1008x=0

We add all the numbers together, and all the variables

(-33516x^2)+16422x=0

We get rid of parentheses

-33516x^2+16422x=0

a = -33516; b = 16422; c = 0;
Δ = b2-4ac
Δ = 164222-4·(-33516)·0
Δ = 269682084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{269682084}=16422$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16422)-16422}{2*-33516}=\frac{-32844}{-67032}
=391/798
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16422)+16422}{2*-33516}=\frac{0}{-67032}
=0
$