3/4n-5=2/5n-4

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

3/4n-5=2/5n-4

We move all terms to the left:

3/4n-5-(2/5n-4)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 5n-4)!=0

n∈R


We get rid of parentheses

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

We calculate fractions


15n/20n^2+(-8n)/20n^2+4-5=0

We add all the numbers together, and all the variables

15n/20n^2+(-8n)/20n^2-1=0

We multiply all the terms by the denominator


15n+(-8n)-1*20n^2=0

Wy multiply elements

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

We get rid of parentheses

-20n^2+15n-8n=0

We add all the numbers together, and all the variables

-20n^2+7n=0

a = -20; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-20)·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*-20}=\frac{-14}{-40}
=7/20
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-20}=\frac{0}{-40}
=0
$