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 add all the numbers together, and all the variables

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

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

Wy multiply elements

-77w^2+21w+(-4w)=0

We get rid of parentheses

-77w^2+21w-4w=0

We add all the numbers together, and all the variables

-77w^2+17w=0

a = -77; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-77)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-77}=\frac{-34}{-154}
=17/77
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-77}=\frac{0}{-154}
=0
$