3/5n+4=1/2n+8

Solution for 3/5n+4=1/2n+8 equation:

3/5n+4=1/2n+8

We move all terms to the left:

3/5n+4-(1/2n+8)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R



Domain of the equation: 2n+8)!=0

n∈R


We get rid of parentheses

3/5n-1/2n-8+4=0

We calculate fractions


6n/10n^2+(-5n)/10n^2-8+4=0

We add all the numbers together, and all the variables

6n/10n^2+(-5n)/10n^2-4=0

We multiply all the terms by the denominator


6n+(-5n)-4*10n^2=0

Wy multiply elements

-40n^2+6n+(-5n)=0

We get rid of parentheses

-40n^2+6n-5n=0

We add all the numbers together, and all the variables

-40n^2+n=0

a = -40; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-40)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-40}=\frac{-2}{-80}
=1/40
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-40}=\frac{0}{-80}
=0
$