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3.4w-11=-4/7w
We move all terms to the left:
3.4w-11-(-4/7w)=0
Domain of the equation: 7w)!=0We get rid of parentheses
w!=0/1
w!=0
w∈R
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} $
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