48/n+16-4n=12

Solution for 48/n+16-4n=12 equation:

48/n+16-4n=12

We move all terms to the left:

48/n+16-4n-(12)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

-4n+48/n+4=0

We multiply all the terms by the denominator


-4n*n+4*n+48=0

We add all the numbers together, and all the variables

4n-4n*n+48=0

Wy multiply elements

-4n^2+4n+48=0

a = -4; b = 4; c = +48;
Δ = b2-4ac
Δ = 42-4·(-4)·48
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-28}{2*-4}=\frac{-32}{-8}
=+4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+28}{2*-4}=\frac{24}{-8}
=-3
$