1/3w-11=-4/7w

Solution for 1/3w-11=-4/7w equation:

1/3w-11=-4/7w

We move all terms to the left:

1/3w-11-(-4/7w)=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 get rid of parentheses

1/3w+4/7w-11=0

We calculate fractions


7w/21w^2+12w/21w^2-11=0

We multiply all the terms by the denominator


7w+12w-11*21w^2=0

We add all the numbers together, and all the variables

19w-11*21w^2=0

Wy multiply elements

-231w^2+19w=0

a = -231; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-231)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-231}=\frac{-38}{-462}
=19/231
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-231}=\frac{0}{-462}
=0
$