2/3x+1/7x=16/21

Solution for 2/3x+1/7x=16/21 equation:

2/3x+1/7x=16/21

We move all terms to the left:

2/3x+1/7x-(16/21)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x+1/7x-(+16/21)=0

We get rid of parentheses

2/3x+1/7x-16/21=0

We calculate fractions


(-2352x^2)/882x^2+588x/882x^2+126x/882x^2=0

We multiply all the terms by the denominator


(-2352x^2)+588x+126x=0

We add all the numbers together, and all the variables

(-2352x^2)+714x=0

We get rid of parentheses

-2352x^2+714x=0

a = -2352; b = 714; c = 0;
Δ = b2-4ac
Δ = 7142-4·(-2352)·0
Δ = 509796
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{509796}=714$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(714)-714}{2*-2352}=\frac{-1428}{-4704}
=17/56
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(714)+714}{2*-2352}=\frac{0}{-4704}
=0
$