1/21-7/3x+6=1/7x=14

Solution for 1/21-7/3x+6=1/7x=14 equation:

1/21-7/3x+6=1/7x=14

We move all terms to the left:

1/21-7/3x+6-(1/7x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-7/3x-(+1/7x)+6+1/21=0

We get rid of parentheses

-7/3x-1/7x+6+1/21=0

We calculate fractions


147x^2/882x^2+(-2058x)/882x^2+(-126x)/882x^2+6=0

We multiply all the terms by the denominator


147x^2+(-2058x)+(-126x)+6*882x^2=0

Wy multiply elements

147x^2+5292x^2+(-2058x)+(-126x)=0

We get rid of parentheses

147x^2+5292x^2-2058x-126x=0

We add all the numbers together, and all the variables

5439x^2-2184x=0

a = 5439; b = -2184; c = 0;
Δ = b2-4ac
Δ = -21842-4·5439·0
Δ = 4769856
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4769856}=2184$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2184)-2184}{2*5439}=\frac{0}{10878}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2184)+2184}{2*5439}=\frac{4368}{10878}
=104/259
$