-7/4n+1/5n=-31/100

Solution for -7/4n+1/5n=-31/100 equation:

-7/4n+1/5n=-31/100

We move all terms to the left:

-7/4n+1/5n-(-31/100)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We get rid of parentheses

-7/4n+1/5n+31/100=0

We calculate fractions


3100n^2/2000n^2+(-3500n)/2000n^2+400n/2000n^2=0

We multiply all the terms by the denominator


3100n^2+(-3500n)+400n=0

We add all the numbers together, and all the variables

3100n^2+400n+(-3500n)=0

We get rid of parentheses

3100n^2+400n-3500n=0

We add all the numbers together, and all the variables

3100n^2-3100n=0

a = 3100; b = -3100; c = 0;
Δ = b2-4ac
Δ = -31002-4·3100·0
Δ = 9610000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9610000}=3100$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3100)-3100}{2*3100}=\frac{0}{6200}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3100)+3100}{2*3100}=\frac{6200}{6200}
=1
$