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

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

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

We move all terms to the left:

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


Domain of the equation: 7w!=0

w!=0/7

w!=0

w∈R



Domain of the equation: 3w)!=0

w!=0/1

w!=0

w∈R


We get rid of parentheses

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

We calculate fractions


9w/21w^2+28w/21w^2-11=0

We multiply all the terms by the denominator


9w+28w-11*21w^2=0

We add all the numbers together, and all the variables

37w-11*21w^2=0

Wy multiply elements

-231w^2+37w=0

a = -231; b = 37; c = 0;
Δ = b2-4ac
Δ = 372-4·(-231)·0
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-37}{2*-231}=\frac{-74}{-462}
=37/231
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+37}{2*-231}=\frac{0}{-462}
=0
$