0.5n^2-12.5-50=0

Solution for 0.5n^2-12.5-50=0 equation:

0.5n^2-12.5-50=0

We add all the numbers together, and all the variables

0.5n^2-62.5=0

a = 0.5; b = 0; c = -62.5;
Δ = b2-4ac
Δ = 02-4·0.5·(-62.5)
Δ = 125
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:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-5\sqrt{5}}{2*0.5}=\frac{0-5\sqrt{5}}{1}
=-\frac{5\sqrt{5}}{1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+5\sqrt{5}}{2*0.5}=\frac{0+5\sqrt{5}}{1}
=\frac{5\sqrt{5}}{1}
$