-7/2w+1/6=-4/3w-7

Solution for -7/2w+1/6=-4/3w-7 equation:

-7/2w+1/6=-4/3w-7

We move all terms to the left:

-7/2w+1/6-(-4/3w-7)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 3w-7)!=0

w∈R


We get rid of parentheses

-7/2w+4/3w+7+1/6=0

We calculate fractions


18w^2/216w^2+(-756w)/216w^2+288w/216w^2+7=0

We multiply all the terms by the denominator


18w^2+(-756w)+288w+7*216w^2=0

We add all the numbers together, and all the variables

18w^2+288w+(-756w)+7*216w^2=0

Wy multiply elements

18w^2+1512w^2+288w+(-756w)=0

We get rid of parentheses

18w^2+1512w^2+288w-756w=0

We add all the numbers together, and all the variables

1530w^2-468w=0

a = 1530; b = -468; c = 0;
Δ = b2-4ac
Δ = -4682-4·1530·0
Δ = 219024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{219024}=468$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-468)-468}{2*1530}=\frac{0}{3060}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-468)+468}{2*1530}=\frac{936}{3060}
=26/85
$