6+4/5n=9/10n

Solution for 6+4/5n=9/10n equation:

6+4/5n=9/10n

We move all terms to the left:

6+4/5n-(9/10n)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R



Domain of the equation: 10n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

4/5n-(+9/10n)+6=0

We get rid of parentheses

4/5n-9/10n+6=0

We calculate fractions


40n/50n^2+(-45n)/50n^2+6=0

We multiply all the terms by the denominator


40n+(-45n)+6*50n^2=0

Wy multiply elements

300n^2+40n+(-45n)=0

We get rid of parentheses

300n^2+40n-45n=0

We add all the numbers together, and all the variables

300n^2-5n=0

a = 300; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·300·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*300}=\frac{0}{600}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*300}=\frac{10}{600}
=1/60
$