(n/7)-(5n/14)=(1/7)

Solution for (n/7)-(5n/14)=(1/7) equation:

(n/7)-(5n/14)=(1/7)

We move all terms to the left:

(n/7)-(5n/14)-((1/7))=0

We add all the numbers together, and all the variables

(+n/7)-(+5n/14)-((+1/7))=0

We get rid of parentheses

n/7-5n/14-((+1/7))=0

We calculate fractions


(-1715n^2)/()+14n/()+()/()=0

We add all the numbers together, and all the variables

(-1715n^2)/()+14n/()+1=0

We multiply all the terms by the denominator


(-1715n^2)+14n+1*()=0

We add all the numbers together, and all the variables

(-1715n^2)+14n=0

We get rid of parentheses

-1715n^2+14n=0

a = -1715; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-1715)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-1715}=\frac{-28}{-3430}
=2/245
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-1715}=\frac{0}{-3430}
=0
$