2n(n+2)+6n-3=-5

Solution for 2n(n+2)+6n-3=-5 equation:

2n(n+2)+6n-3=-5

We move all terms to the left:

2n(n+2)+6n-3-(-5)=0

We add all the numbers together, and all the variables

6n+2n(n+2)+2=0

We multiply parentheses

2n^2+6n+4n+2=0

We add all the numbers together, and all the variables

2n^2+10n+2=0

a = 2; b = 10; c = +2;
Δ = b2-4ac
Δ = 102-4·2·2
Δ = 84
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{21}}{2*2}=\frac{-10-2\sqrt{21}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{21}}{2*2}=\frac{-10+2\sqrt{21}}{4}
$