n(1/2n+0.5)=36

Solution for n(1/2n+0.5)=36 equation:

n(1/2n+0.5)=36

We move all terms to the left:

n(1/2n+0.5)-(36)=0


Domain of the equation: 2n+0.5)!=0

n∈R


We multiply parentheses

n^2+0.5n-36=0

a = 1; b = 0.5; c = -36;
Δ = b2-4ac
Δ = 0.52-4·1·(-36)
Δ = 144.25
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{144.25}}{2*1}=\frac{-0.5-\sqrt{144.25}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.5)+\sqrt{144.25}}{2*1}=\frac{-0.5+\sqrt{144.25}}{2}
$