3/7w-11=-4/5w

Solution for 3/7w-11=-4/5w equation:

3/7w-11=-4/5w

We move all terms to the left:

3/7w-11-(-4/5w)=0


Domain of the equation: 7w!=0

w!=0/7

w!=0

w∈R



Domain of the equation: 5w)!=0

w!=0/1

w!=0

w∈R


We get rid of parentheses

3/7w+4/5w-11=0

We calculate fractions


15w/35w^2+28w/35w^2-11=0

We multiply all the terms by the denominator


15w+28w-11*35w^2=0

We add all the numbers together, and all the variables

43w-11*35w^2=0

Wy multiply elements

-385w^2+43w=0

a = -385; b = 43; c = 0;
Δ = b2-4ac
Δ = 432-4·(-385)·0
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-43}{2*-385}=\frac{-86}{-770}
=43/385
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+43}{2*-385}=\frac{0}{-770}
=0
$