2/5n+6=3/4n-8

Solution for 2/5n+6=3/4n-8 equation:

2/5n+6=3/4n-8

We move all terms to the left:

2/5n+6-(3/4n-8)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R



Domain of the equation: 4n-8)!=0

n∈R


We get rid of parentheses

2/5n-3/4n+8+6=0

We calculate fractions


8n/20n^2+(-15n)/20n^2+8+6=0

We add all the numbers together, and all the variables

8n/20n^2+(-15n)/20n^2+14=0

We multiply all the terms by the denominator


8n+(-15n)+14*20n^2=0

Wy multiply elements

280n^2+8n+(-15n)=0

We get rid of parentheses

280n^2+8n-15n=0

We add all the numbers together, and all the variables

280n^2-7n=0

a = 280; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·280·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*280}=\frac{0}{560}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*280}=\frac{14}{560}
=1/40
$