5n^2+10n=O(n^2)

Solution for 5n^2+10n=O(n^2) equation:

5n^2+10n=(n^2)

We move all terms to the left:

5n^2+10n-((n^2))=0

determiningTheFunctionDomain
5n^2+10n-n^2=0

We add all the numbers together, and all the variables

5n^2-n^2+10n=0

We add all the numbers together, and all the variables

4n^2+10n=0

a = 4; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·4·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*4}=\frac{-20}{8}
=-2+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*4}=\frac{0}{8}
=0
$