3/n-1/4n=40

Solution for 3/n-1/4n=40 equation:

3/n-1/4n=40

We move all terms to the left:

3/n-1/4n-(40)=0


Domain of the equation: n!=0

n∈R



Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We calculate fractions


12n/4n^2+(-n)/4n^2-40=0

We add all the numbers together, and all the variables

12n/4n^2+(-1n)/4n^2-40=0

We multiply all the terms by the denominator


12n+(-1n)-40*4n^2=0

Wy multiply elements

-160n^2+12n+(-1n)=0

We get rid of parentheses

-160n^2+12n-1n=0

We add all the numbers together, and all the variables

-160n^2+11n=0

a = -160; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-160)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-160}=\frac{-22}{-320}
=11/160
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-160}=\frac{0}{-320}
=0
$