4/1+3n=4/5n+12

Solution for 4/1+3n=4/5n+12 equation:

4/1+3n=4/5n+12

We move all terms to the left:

4/1+3n-(4/5n+12)=0


Domain of the equation: 5n+12)!=0

n∈R


We add all the numbers together, and all the variables

3n-(4/5n+12)=0

We get rid of parentheses

3n-4/5n-12=0

We multiply all the terms by the denominator


3n*5n-12*5n-4=0

Wy multiply elements

15n^2-60n-4=0

a = 15; b = -60; c = -4;
Δ = b2-4ac
Δ = -602-4·15·(-4)
Δ = 3840
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:

$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-16\sqrt{15}}{2*15}=\frac{60-16\sqrt{15}}{30}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+16\sqrt{15}}{2*15}=\frac{60+16\sqrt{15}}{30}
$