n=0.5;8/n+8

Solution for n=0.5;8/n+8 equation:

n=0.58/n+8

We move all terms to the left:

n-(0.58/n+8)=0


Domain of the equation: n+8)!=0

n∈R


We get rid of parentheses

n-0.58/n-8=0

We multiply all the terms by the denominator


n*n-8*n-0.58=0

We add all the numbers together, and all the variables

-8n+n*n-0.58=0

Wy multiply elements

n^2-8n-0.58=0

a = 1; b = -8; c = -0.58;
Δ = b2-4ac
Δ = -82-4·1·(-0.58)
Δ = 66.32
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{-(-8)-\sqrt{66.32}}{2*1}=\frac{8-\sqrt{66.32}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+\sqrt{66.32}}{2*1}=\frac{8+\sqrt{66.32}}{2}
$