(n/5)-(7n/10)=(1/5)

Solution for (n/5)-(7n/10)=(1/5) equation:

(n/5)-(7n/10)=(1/5)

We move all terms to the left:

(n/5)-(7n/10)-((1/5))=0

We add all the numbers together, and all the variables

(+n/5)-(+7n/10)-((+1/5))=0

We get rid of parentheses

n/5-7n/10-((+1/5))=0

We calculate fractions


(-875n^2)/()+10n/()+()/()=0

We add all the numbers together, and all the variables

(-875n^2)/()+10n/()+1=0

We multiply all the terms by the denominator


(-875n^2)+10n+1*()=0

We add all the numbers together, and all the variables

(-875n^2)+10n=0

We get rid of parentheses

-875n^2+10n=0

a = -875; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-875)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-875}=\frac{-20}{-1750}
=2/175
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-875}=\frac{0}{-1750}
=0
$