3/w-11=-4/7w

Solution for 3/w-11=-4/7w equation:

3/w-11=-4/7w

We move all terms to the left:

3/w-11-(-4/7w)=0


Domain of the equation: w!=0

w∈R



Domain of the equation: 7w)!=0

w!=0/1

w!=0

w∈R


We get rid of parentheses

3/w+4/7w-11=0

We calculate fractions


21w/7w^2+4w/7w^2-11=0

We multiply all the terms by the denominator


21w+4w-11*7w^2=0

We add all the numbers together, and all the variables

25w-11*7w^2=0

Wy multiply elements

-77w^2+25w=0

a = -77; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-77)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-77}=\frac{-50}{-154}
=25/77
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-77}=\frac{0}{-154}
=0
$