4/3n-1-3n=1

Solution for 4/3n-1-3n=1 equation:

4/3n-1-3n=1

We move all terms to the left:

4/3n-1-3n-(1)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We add all the numbers together, and all the variables

-3n+4/3n-2=0

We multiply all the terms by the denominator


-3n*3n-2*3n+4=0

Wy multiply elements

-9n^2-6n+4=0

a = -9; b = -6; c = +4;
Δ = b2-4ac
Δ = -62-4·(-9)·4
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{5}}{2*-9}=\frac{6-6\sqrt{5}}{-18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{5}}{2*-9}=\frac{6+6\sqrt{5}}{-18}
$