2n^2-100=-10n

Solution for 2n^2-100=-10n equation:

2n^2-100=-10n

We move all terms to the left:

2n^2-100-(-10n)=0

We get rid of parentheses

2n^2+10n-100=0

a = 2; b = 10; c = -100;
Δ = b2-4ac
Δ = 102-4·2·(-100)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-30}{2*2}=\frac{-40}{4}
=-10
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+30}{2*2}=\frac{20}{4}
=5
$