10n(n+3)=n-10

Solution for 10n(n+3)=n-10 equation:

10n(n+3)=n-10

We move all terms to the left:

10n(n+3)-(n-10)=0

We multiply parentheses

10n^2+30n-(n-10)=0

We get rid of parentheses

10n^2+30n-n+10=0

We add all the numbers together, and all the variables

10n^2+29n+10=0

a = 10; b = 29; c = +10;
Δ = b2-4ac
Δ = 292-4·10·10
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-21}{2*10}=\frac{-50}{20}
=-2+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+21}{2*10}=\frac{-8}{20}
=-2/5
$