2n^2=-10n-2

Solution for 2n^2=-10n-2 equation:

2n^2=-10n-2

We move all terms to the left:

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

We get rid of parentheses

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}
$