1/20n+9/10n+9/5=7/6

Solution for 1/20n+9/10n+9/5=7/6 equation:

1/20n+9/10n+9/5=7/6

We move all terms to the left:

1/20n+9/10n+9/5-(7/6)=0


Domain of the equation: 20n!=0

n!=0/20

n!=0

n∈R



Domain of the equation: 10n!=0

n!=0/10

n!=0

n∈R


We add all the numbers together, and all the variables

1/20n+9/10n+9/5-(+7/6)=0

We get rid of parentheses

1/20n+9/10n+9/5-7/6=0

We calculate fractions


(-7000n^2)/30000n^2+10800n^2/30000n^2+1500n/30000n^2+27000n/30000n^2=0

We multiply all the terms by the denominator


(-7000n^2)+10800n^2+1500n+27000n=0

We add all the numbers together, and all the variables

10800n^2+(-7000n^2)+28500n=0

We get rid of parentheses

10800n^2-7000n^2+28500n=0

We add all the numbers together, and all the variables

3800n^2+28500n=0

a = 3800; b = 28500; c = 0;
Δ = b2-4ac
Δ = 285002-4·3800·0
Δ = 812250000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{812250000}=28500$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28500)-28500}{2*3800}=\frac{-57000}{7600}
=-7+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28500)+28500}{2*3800}=\frac{0}{7600}
=0
$