3/8n-1/4n=-4

Solution for 3/8n-1/4n=-4 equation:

3/8n-1/4n=-4

We move all terms to the left:

3/8n-1/4n-(-4)=0


Domain of the equation: 8n!=0

n!=0/8

n!=0

n∈R



Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We add all the numbers together, and all the variables

3/8n-1/4n+4=0

We calculate fractions


12n/32n^2+(-8n)/32n^2+4=0

We multiply all the terms by the denominator


12n+(-8n)+4*32n^2=0

Wy multiply elements

128n^2+12n+(-8n)=0

We get rid of parentheses

128n^2+12n-8n=0

We add all the numbers together, and all the variables

128n^2+4n=0

a = 128; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·128·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*128}=\frac{-8}{256}
=-1/32
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*128}=\frac{0}{256}
=0
$