5/6c+1/3c=2/7

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Solution for 5/6c+1/3c=2/7 equation:



5/6c+1/3c=2/7
We move all terms to the left:
5/6c+1/3c-(2/7)=0
Domain of the equation: 6c!=0
c!=0/6
c!=0
c∈R
Domain of the equation: 3c!=0
c!=0/3
c!=0
c∈R
We add all the numbers together, and all the variables
5/6c+1/3c-(+2/7)=0
We get rid of parentheses
5/6c+1/3c-2/7=0
We calculate fractions
(-108c^2)/882c^2+735c/882c^2+294c/882c^2=0
We multiply all the terms by the denominator
(-108c^2)+735c+294c=0
We add all the numbers together, and all the variables
(-108c^2)+1029c=0
We get rid of parentheses
-108c^2+1029c=0
a = -108; b = 1029; c = 0;
Δ = b2-4ac
Δ = 10292-4·(-108)·0
Δ = 1058841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1058841}=1029$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1029)-1029}{2*-108}=\frac{-2058}{-216} =9+19/36 $
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1029)+1029}{2*-108}=\frac{0}{-216} =0 $

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