n^2+100n+50=0

Solution for n^2+100n+50=0 equation:

n^2+100n+50=0

a = 1; b = 100; c = +50;
Δ = b2-4ac
Δ = 1002-4·1·50
Δ = 9800
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:

$\sqrt{\Delta}=\sqrt{9800}=\sqrt{4900*2}=\sqrt{4900}*\sqrt{2}=70\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-70\sqrt{2}}{2*1}=\frac{-100-70\sqrt{2}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+70\sqrt{2}}{2*1}=\frac{-100+70\sqrt{2}}{2}
$