-2n(n+3)=-10

Solution for -2n(n+3)=-10 equation:

-2n(n+3)=-10

We move all terms to the left:

-2n(n+3)-(-10)=0

We add all the numbers together, and all the variables

-2n(n+3)+10=0

We multiply parentheses

-2n^2-6n+10=0

a = -2; b = -6; c = +10;
Δ = b2-4ac
Δ = -62-4·(-2)·10
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{29}}{2*-2}=\frac{6-2\sqrt{29}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{29}}{2*-2}=\frac{6+2\sqrt{29}}{-4}
$