2/3w-6=5/7w

Solution for 2/3w-6=5/7w equation:

2/3w-6=5/7w

We move all terms to the left:

2/3w-6-(5/7w)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 7w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

2/3w-(+5/7w)-6=0

We get rid of parentheses

2/3w-5/7w-6=0

We calculate fractions


14w/21w^2+(-15w)/21w^2-6=0

We multiply all the terms by the denominator


14w+(-15w)-6*21w^2=0

Wy multiply elements

-126w^2+14w+(-15w)=0

We get rid of parentheses

-126w^2+14w-15w=0

We add all the numbers together, and all the variables

-126w^2-1w=0

a = -126; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-126)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-126}=\frac{0}{-252}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-126}=\frac{2}{-252}
=-1/126
$