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

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

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

We move all terms to the left:

5/6c+1/3c-(1/7)=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-(+1/7)=0

We get rid of parentheses

5/6c+1/3c-1/7=0

We calculate fractions


(-54c^2)/882c^2+735c/882c^2+294c/882c^2=0

We multiply all the terms by the denominator


(-54c^2)+735c+294c=0

We add all the numbers together, and all the variables

(-54c^2)+1029c=0

We get rid of parentheses

-54c^2+1029c=0

a = -54; b = 1029; c = 0;
Δ = b2-4ac
Δ = 10292-4·(-54)·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*-54}=\frac{-2058}{-108}
=19+1/18
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1029)+1029}{2*-54}=\frac{0}{-108}
=0
$