n/2.3n+4.98=3n+2.6

Solution for n/2.3n+4.98=3n+2.6 equation:

n/2.3n+4.98=3n+2.6

We move all terms to the left:

n/2.3n+4.98-(3n+2.6)=0


Domain of the equation: 2.3n!=0

n!=0/2.3

n!=0

n∈R


We get rid of parentheses

n/2.3n-3n-2.6+4.98=0

We multiply all the terms by the denominator


n-3n*2.3n-(2.6)*2.3n+(4.98)*2.3n=0

We multiply parentheses

n-3n*2.3n-5.2n+9.96n=0

Wy multiply elements

-6n^2+n-5.2n+9.96n=0

We add all the numbers together, and all the variables

-6n^2+5.76n=0

a = -6; b = 5.76; c = 0;
Δ = b2-4ac
Δ = 5.762-4·(-6)·0
Δ = 33.1776
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{-(5.76)-\sqrt{33.1776}}{2*-6}=\frac{-5.76-\sqrt{33.1776}}{-12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.76)+\sqrt{33.1776}}{2*-6}=\frac{-5.76+\sqrt{33.1776}}{-12}
$