0.5n^2-0.5n-100=0

Solution for 0.5n^2-0.5n-100=0 equation:

0.5n^2-0.5n-100=0

a = 0.5; b = -0.5; c = -100;
Δ = b2-4ac
Δ = -0.52-4·0.5·(-100)
Δ = 200.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.5)-\sqrt{200.25}}{2*0.5}=\frac{0.5-\sqrt{200.25}}{1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{200.25}}{2*0.5}=\frac{0.5+\sqrt{200.25}}{1}
$