4/3n-2n=3

Solution for 4/3n-2n=3 equation:

4/3n-2n=3

We move all terms to the left:

4/3n-2n-(3)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -6; b = -9; c = +4;
Δ = b2-4ac
Δ = -92-4·(-6)·4
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{177}}{2*-6}=\frac{9-\sqrt{177}}{-12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{177}}{2*-6}=\frac{9+\sqrt{177}}{-12}
$