9/7w=13/14w+12

Solution for 9/7w=13/14w+12 equation:

9/7w=13/14w+12

We move all terms to the left:

9/7w-(13/14w+12)=0


Domain of the equation: 7w!=0

w!=0/7

w!=0

w∈R



Domain of the equation: 14w+12)!=0

w∈R


We get rid of parentheses

9/7w-13/14w-12=0

We calculate fractions


126w/98w^2+(-91w)/98w^2-12=0

We multiply all the terms by the denominator


126w+(-91w)-12*98w^2=0

Wy multiply elements

-1176w^2+126w+(-91w)=0

We get rid of parentheses

-1176w^2+126w-91w=0

We add all the numbers together, and all the variables

-1176w^2+35w=0

a = -1176; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·(-1176)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*-1176}=\frac{-70}{-2352}
=5/168
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*-1176}=\frac{0}{-2352}
=0
$