n^2+6n-200=0

Solution for n^2+6n-200=0 equation:

n^2+6n-200=0

a = 1; b = 6; c = -200;
Δ = b2-4ac
Δ = 62-4·1·(-200)
Δ = 836
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:

$\sqrt{\Delta}=\sqrt{836}=\sqrt{4*209}=\sqrt{4}*\sqrt{209}=2\sqrt{209}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{209}}{2*1}=\frac{-6-2\sqrt{209}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{209}}{2*1}=\frac{-6+2\sqrt{209}}{2}
$