8/7x-3/14=1/3x

Solution for 8/7x-3/14=1/3x equation:

8/7x-3/14=1/3x

We move all terms to the left:

8/7x-3/14-(1/3x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8/7x-(+1/3x)-3/14=0

We get rid of parentheses

8/7x-1/3x-3/14=0

We calculate fractions


(-189x^2)/294x^2+336x/294x^2+(-98x)/294x^2=0

We multiply all the terms by the denominator


(-189x^2)+336x+(-98x)=0

We get rid of parentheses

-189x^2+336x-98x=0

We add all the numbers together, and all the variables

-189x^2+238x=0

a = -189; b = 238; c = 0;
Δ = b2-4ac
Δ = 2382-4·(-189)·0
Δ = 56644
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{56644}=238$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(238)-238}{2*-189}=\frac{-476}{-378}
=1+7/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(238)+238}{2*-189}=\frac{0}{-378}
=0
$