3/4n=-13/5n-18

Solution for 3/4n=-13/5n-18 equation:

3/4n=-13/5n-18

We move all terms to the left:

3/4n-(-13/5n-18)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 5n-18)!=0

n∈R


We get rid of parentheses

3/4n+13/5n+18=0

We calculate fractions


15n/20n^2+52n/20n^2+18=0

We multiply all the terms by the denominator


15n+52n+18*20n^2=0

We add all the numbers together, and all the variables

67n+18*20n^2=0

Wy multiply elements

360n^2+67n=0

a = 360; b = 67; c = 0;
Δ = b2-4ac
Δ = 672-4·360·0
Δ = 4489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4489}=67$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(67)-67}{2*360}=\frac{-134}{720}
=-67/360
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(67)+67}{2*360}=\frac{0}{720}
=0
$