2/3x+6/7x=8-2

Solution for 2/3x+6/7x=8-2 equation:

2/3x+6/7x=8-2

We move all terms to the left:

2/3x+6/7x-(8-2)=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+6/7x-6=0

We calculate fractions


14x/21x^2+18x/21x^2-6=0

We multiply all the terms by the denominator


14x+18x-6*21x^2=0

We add all the numbers together, and all the variables

32x-6*21x^2=0

Wy multiply elements

-126x^2+32x=0

a = -126; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·(-126)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*-126}=\frac{-64}{-252}
=16/63
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*-126}=\frac{0}{-252}
=0
$