14/15c+1/5c=1/7

Solution for 14/15c+1/5c=1/7 equation:

14/15c+1/5c=1/7

We move all terms to the left:

14/15c+1/5c-(1/7)=0


Domain of the equation: 15c!=0

c!=0/15

c!=0

c∈R



Domain of the equation: 5c!=0

c!=0/5

c!=0

c∈R


We add all the numbers together, and all the variables

14/15c+1/5c-(+1/7)=0

We get rid of parentheses

14/15c+1/5c-1/7=0

We calculate fractions


(-375c^2)/3675c^2+3430c/3675c^2+735c/3675c^2=0

We multiply all the terms by the denominator


(-375c^2)+3430c+735c=0

We add all the numbers together, and all the variables

(-375c^2)+4165c=0

We get rid of parentheses

-375c^2+4165c=0

a = -375; b = 4165; c = 0;
Δ = b2-4ac
Δ = 41652-4·(-375)·0
Δ = 17347225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17347225}=4165$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4165)-4165}{2*-375}=\frac{-8330}{-750}
=11+8/75
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4165)+4165}{2*-375}=\frac{0}{-750}
=0
$