-2n^2-30n+800=0

Solution for -2n^2-30n+800=0 equation:

-2n^2-30n+800=0

a = -2; b = -30; c = +800;
Δ = b2-4ac
Δ = -302-4·(-2)·800
Δ = 7300
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:

$\sqrt{\Delta}=\sqrt{7300}=\sqrt{100*73}=\sqrt{100}*\sqrt{73}=10\sqrt{73}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{73}}{2*-2}=\frac{30-10\sqrt{73}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{73}}{2*-2}=\frac{30+10\sqrt{73}}{-4}
$