3/4n-16=14-1/2n

Solution for 3/4n-16=14-1/2n equation:

3/4n-16=14-1/2n

We move all terms to the left:

3/4n-16-(14-1/2n)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 2n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

3/4n-(-1/2n+14)-16=0

We get rid of parentheses

3/4n+1/2n-14-16=0

We calculate fractions


6n/8n^2+4n/8n^2-14-16=0

We add all the numbers together, and all the variables

6n/8n^2+4n/8n^2-30=0

We multiply all the terms by the denominator


6n+4n-30*8n^2=0

We add all the numbers together, and all the variables

10n-30*8n^2=0

Wy multiply elements

-240n^2+10n=0

a = -240; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-240)·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*-240}=\frac{-20}{-480}
=1/24
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-240}=\frac{0}{-480}
=0
$