n=6.40/n+6

Solution for n=6.40/n+6 equation:

n=6.40/n+6

We move all terms to the left:

n-(6.40/n+6)=0


Domain of the equation: n+6)!=0

n∈R


We get rid of parentheses

n-6.40/n-6=0

We multiply all the terms by the denominator


n*n-6*n-6.40=0

We add all the numbers together, and all the variables

-6n+n*n-6.4=0

Wy multiply elements

n^2-6n-6.4=0

a = 1; b = -6; c = -6.4;
Δ = b2-4ac
Δ = -62-4·1·(-6.4)
Δ = 61.6
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{-(-6)-\sqrt{61.6}}{2*1}=\frac{6-\sqrt{61.6}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+\sqrt{61.6}}{2*1}=\frac{6+\sqrt{61.6}}{2}
$