3/5n-18=1/4n-4

Solution for 3/5n-18=1/4n-4 equation:

3/5n-18=1/4n-4

We move all terms to the left:

3/5n-18-(1/4n-4)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R



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

n∈R


We get rid of parentheses

3/5n-1/4n+4-18=0

We calculate fractions


12n/20n^2+(-5n)/20n^2+4-18=0

We add all the numbers together, and all the variables

12n/20n^2+(-5n)/20n^2-14=0

We multiply all the terms by the denominator


12n+(-5n)-14*20n^2=0

Wy multiply elements

-280n^2+12n+(-5n)=0

We get rid of parentheses

-280n^2+12n-5n=0

We add all the numbers together, and all the variables

-280n^2+7n=0

a = -280; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-280)·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*-280}=\frac{-14}{-560}
=1/40
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-280}=\frac{0}{-560}
=0
$