3/4n=5+1/2n

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

3/4n=5+1/2n

We move all terms to the left:

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


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 2n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

-40n^2+6n+(-4n)=0

We get rid of parentheses

-40n^2+6n-4n=0

We add all the numbers together, and all the variables

-40n^2+2n=0

a = -40; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-40)·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*-40}=\frac{-4}{-80}
=1/20
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-40}=\frac{0}{-80}
=0
$