7/11w+4/w=1

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Solution for 7/11w+4/w=1 equation:



7/11w+4/w=1
We move all terms to the left:
7/11w+4/w-(1)=0
Domain of the equation: 11w!=0
w!=0/11
w!=0
w∈R
Domain of the equation: w!=0
w∈R
We calculate fractions
7w/11w^2+44w/11w^2-1=0
We multiply all the terms by the denominator
7w+44w-1*11w^2=0
We add all the numbers together, and all the variables
51w-1*11w^2=0
Wy multiply elements
-11w^2+51w=0
a = -11; b = 51; c = 0;
Δ = b2-4ac
Δ = 512-4·(-11)·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-51}{2*-11}=\frac{-102}{-22} =4+7/11 $
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+51}{2*-11}=\frac{0}{-22} =0 $

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