2.3+3n=4/5n+12

Solution for 2.3+3n=4/5n+12 equation:

2.3+3n=4/5n+12

We move all terms to the left:

2.3+3n-(4/5n+12)=0


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

n∈R


We get rid of parentheses

3n-4/5n-12+2.3=0

We multiply all the terms by the denominator


3n*5n-12*5n+(2.3)*5n-4=0

We multiply parentheses

3n*5n-12*5n+11.5n-4=0

Wy multiply elements

15n^2-60n+11.5n-4=0

We add all the numbers together, and all the variables

15n^2-48.5n-4=0

a = 15; b = -48.5; c = -4;
Δ = b2-4ac
Δ = -48.52-4·15·(-4)
Δ = 2592.25
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{-(-48.5)-\sqrt{2592.25}}{2*15}=\frac{48.5-\sqrt{2592.25}}{30}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48.5)+\sqrt{2592.25}}{2*15}=\frac{48.5+\sqrt{2592.25}}{30}
$