1/5c+2/7=2-1/7c

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

1/5c+2/7=2-1/7c

We move all terms to the left:

1/5c+2/7-(2-1/7c)=0


Domain of the equation: 5c!=0

c!=0/5

c!=0

c∈R



Domain of the equation: 7c)!=0

c!=0/1

c!=0

c∈R


We add all the numbers together, and all the variables

1/5c-(-1/7c+2)+2/7=0

We get rid of parentheses

1/5c+1/7c-2+2/7=0

We calculate fractions


343c/1715c^2+5c/1715c^2+10c/1715c^2-2=0

We multiply all the terms by the denominator


343c+5c+10c-2*1715c^2=0

We add all the numbers together, and all the variables

358c-2*1715c^2=0

Wy multiply elements

-3430c^2+358c=0

a = -3430; b = 358; c = 0;
Δ = b2-4ac
Δ = 3582-4·(-3430)·0
Δ = 128164
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{128164}=358$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(358)-358}{2*-3430}=\frac{-716}{-6860}
=179/1715
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(358)+358}{2*-3430}=\frac{0}{-6860}
=0
$