1.66+3n=4/5n+15

Solution for 1.66+3n=4/5n+15 equation:

1.66+3n=4/5n+15

We move all terms to the left:

1.66+3n-(4/5n+15)=0


Domain of the equation: 5n+15)!=0

n∈R


We get rid of parentheses

3n-4/5n-15+1.66=0

We multiply all the terms by the denominator


3n*5n-15*5n+(1.66)*5n-4=0

We multiply parentheses

3n*5n-15*5n+8.3n-4=0

Wy multiply elements

15n^2-75n+8.3n-4=0

We add all the numbers together, and all the variables

15n^2-66.7n-4=0

a = 15; b = -66.7; c = -4;
Δ = b2-4ac
Δ = -66.72-4·15·(-4)
Δ = 4688.89
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{-(-66.7)-\sqrt{4688.89}}{2*15}=\frac{66.7-\sqrt{4688.89}}{30}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66.7)+\sqrt{4688.89}}{2*15}=\frac{66.7+\sqrt{4688.89}}{30}
$