1/2n+3/4n=12

Solution for 1/2n+3/4n=12 equation:

1/2n+3/4n=12

We move all terms to the left:

1/2n+3/4n-(12)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We calculate fractions


4n/8n^2+6n/8n^2-12=0

We multiply all the terms by the denominator


4n+6n-12*8n^2=0

We add all the numbers together, and all the variables

10n-12*8n^2=0

Wy multiply elements

-96n^2+10n=0

a = -96; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-96)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-96}=\frac{-20}{-192}
=5/48
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-96}=\frac{0}{-192}
=0
$