0.5n^2+0.5n=78

Solution for 0.5n^2+0.5n=78 equation:

0.5n^2+0.5n=78

We move all terms to the left:

0.5n^2+0.5n-(78)=0

a = 0.5; b = 0.5; c = -78;
Δ = b2-4ac
Δ = 0.52-4·0.5·(-78)
Δ = 156.25
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{156.25}}{2*0.5}=\frac{-0.5-\sqrt{156.25}}{1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.5)+\sqrt{156.25}}{2*0.5}=\frac{-0.5+\sqrt{156.25}}{1}
$