36+1/6n=1/4n+21

Solution for 36+1/6n=1/4n+21 equation:

36+1/6n=1/4n+21

We move all terms to the left:

36+1/6n-(1/4n+21)=0


Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R



Domain of the equation: 4n+21)!=0

n∈R


We get rid of parentheses

1/6n-1/4n-21+36=0

We calculate fractions


4n/24n^2+(-6n)/24n^2-21+36=0

We add all the numbers together, and all the variables

4n/24n^2+(-6n)/24n^2+15=0

We multiply all the terms by the denominator


4n+(-6n)+15*24n^2=0

Wy multiply elements

360n^2+4n+(-6n)=0

We get rid of parentheses

360n^2+4n-6n=0

We add all the numbers together, and all the variables

360n^2-2n=0

a = 360; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·360·0
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*360}=\frac{0}{720}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*360}=\frac{4}{720}
=1/180
$