4n-9.5=1/5n+1.8

Solution for 4n-9.5=1/5n+1.8 equation:

4n-9.5=1/5n+1.8

We move all terms to the left:

4n-9.5-(1/5n+1.8)=0


Domain of the equation: 5n+1.8)!=0

n∈R


We get rid of parentheses

4n-1/5n-1.8-9.5=0

We multiply all the terms by the denominator


4n*5n-(1.8)*5n-(9.5)*5n-1=0

We multiply parentheses

4n*5n-9n-47.5n-1=0

Wy multiply elements

20n^2-9n-47.5n-1=0

We add all the numbers together, and all the variables

20n^2-56.5n-1=0

a = 20; b = -56.5; c = -1;
Δ = b2-4ac
Δ = -56.52-4·20·(-1)
Δ = 3272.25
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{-(-56.5)-\sqrt{3272.25}}{2*20}=\frac{56.5-\sqrt{3272.25}}{40}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56.5)+\sqrt{3272.25}}{2*20}=\frac{56.5+\sqrt{3272.25}}{40}
$