3/4n=7/1n-18

Solution for 3/4n=7/1n-18 equation:

3/4n=7/1n-18

We move all terms to the left:

3/4n-(7/1n-18)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 1n-18)!=0

n∈R


We get rid of parentheses

3/4n-7/1n+18=0

We calculate fractions


3n/4n^2+(-28n)/4n^2+18=0

We multiply all the terms by the denominator


3n+(-28n)+18*4n^2=0

Wy multiply elements

72n^2+3n+(-28n)=0

We get rid of parentheses

72n^2+3n-28n=0

We add all the numbers together, and all the variables

72n^2-25n=0

a = 72; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·72·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*72}=\frac{0}{144}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*72}=\frac{50}{144}
=25/72
$