-.5x^2-5x+1600=0

Solution for -.5x^2-5x+1600=0 equation:

-.5x^2-5x+1600=0

We add all the numbers together, and all the variables

-0.5x^2-5x+1600=0

a = -0.5; b = -5; c = +1600;
Δ = b2-4ac
Δ = -52-4·(-0.5)·1600
Δ = 3225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3225}=\sqrt{25*129}=\sqrt{25}*\sqrt{129}=5\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{129}}{2*-0.5}=\frac{5-5\sqrt{129}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{129}}{2*-0.5}=\frac{5+5\sqrt{129}}{-1}
$