1/8n+35=-1/4n+41

Solution for 1/8n+35=-1/4n+41 equation:

1/8n+35=-1/4n+41

We move all terms to the left:

1/8n+35-(-1/4n+41)=0


Domain of the equation: 8n!=0

n!=0/8

n!=0

n∈R



Domain of the equation: 4n+41)!=0

n∈R


We get rid of parentheses

1/8n+1/4n-41+35=0

We calculate fractions


4n/32n^2+8n/32n^2-41+35=0

We add all the numbers together, and all the variables

4n/32n^2+8n/32n^2-6=0

We multiply all the terms by the denominator


4n+8n-6*32n^2=0

We add all the numbers together, and all the variables

12n-6*32n^2=0

Wy multiply elements

-192n^2+12n=0

a = -192; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-192)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-192}=\frac{-24}{-384}
=1/16
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-192}=\frac{0}{-384}
=0
$