75/5n=12+4n

Solution for 75/5n=12+4n equation:

75/5n=12+4n

We move all terms to the left:

75/5n-(12+4n)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We add all the numbers together, and all the variables

75/5n-(4n+12)=0

We get rid of parentheses

75/5n-4n-12=0

We multiply all the terms by the denominator


-4n*5n-12*5n+75=0

Wy multiply elements

-20n^2-60n+75=0

a = -20; b = -60; c = +75;
Δ = b2-4ac
Δ = -602-4·(-20)·75
Δ = 9600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9600}=\sqrt{1600*6}=\sqrt{1600}*\sqrt{6}=40\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-40\sqrt{6}}{2*-20}=\frac{60-40\sqrt{6}}{-40}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+40\sqrt{6}}{2*-20}=\frac{60+40\sqrt{6}}{-40}
$