3.4w-11=-4/7w

Solution for 3.4w-11=-4/7w equation:

3.4w-11=-4/7w

We move all terms to the left:

3.4w-11-(-4/7w)=0


Domain of the equation: 7w)!=0

w!=0/1

w!=0

w∈R


We get rid of parentheses

3.4w+4/7w-11=0

We multiply all the terms by the denominator


(3.4w)*7w-11*7w+4=0

We add all the numbers together, and all the variables

(+3.4w)*7w-11*7w+4=0

We multiply parentheses

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

Wy multiply elements

21w^2-77w+4=0

a = 21; b = -77; c = +4;
Δ = b2-4ac
Δ = -772-4·21·4
Δ = 5593
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-77)-\sqrt{5593}}{2*21}=\frac{77-\sqrt{5593}}{42}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+\sqrt{5593}}{2*21}=\frac{77+\sqrt{5593}}{42}
$