5n+0.1=5/n-0.4

Solution for 5n+0.1=5/n-0.4 equation:

5n+0.1=5/n-0.4

We move all terms to the left:

5n+0.1-(5/n-0.4)=0


Domain of the equation: n-0.4)!=0

n∈R


We get rid of parentheses

5n-5/n+0.4+0.1=0

We multiply all the terms by the denominator


5n*n+(0.4)*n+(0.1)*n-5=0

We multiply parentheses

5n*n+0.4n+0.1n-5=0

Wy multiply elements

5n^2+0.4n+0.1n-5=0

We add all the numbers together, and all the variables

5n^2+0.5n-5=0

a = 5; b = 0.5; c = -5;
Δ = b2-4ac
Δ = 0.52-4·5·(-5)
Δ = 100.25
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{-(0.5)-\sqrt{100.25}}{2*5}=\frac{-0.5-\sqrt{100.25}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.5)+\sqrt{100.25}}{2*5}=\frac{-0.5+\sqrt{100.25}}{10}
$