3/4n-1=2/2n-5

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

3/4n-1=2/2n-5

We move all terms to the left:

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


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 2n-5)!=0

n∈R


We get rid of parentheses

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

We calculate fractions


6n/8n^2+(-8n)/8n^2+5-1=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


6n+(-8n)+4*8n^2=0

Wy multiply elements

32n^2+6n+(-8n)=0

We get rid of parentheses

32n^2+6n-8n=0

We add all the numbers together, and all the variables

32n^2-2n=0

a = 32; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·32·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*32}=\frac{0}{64}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*32}=\frac{4}{64}
=1/16
$