80=0.5x^2-40x-600

Solution for 80=0.5x^2-40x-600 equation:

80=0.5x^2-40x-600

We move all terms to the left:

80-(0.5x^2-40x-600)=0

We get rid of parentheses

-0.5x^2+40x+600+80=0

We add all the numbers together, and all the variables

-0.5x^2+40x+680=0

a = -0.5; b = 40; c = +680;
Δ = b2-4ac
Δ = 402-4·(-0.5)·680
Δ = 2960
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:

$\sqrt{\Delta}=\sqrt{2960}=\sqrt{16*185}=\sqrt{16}*\sqrt{185}=4\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{185}}{2*-0.5}=\frac{-40-4\sqrt{185}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{185}}{2*-0.5}=\frac{-40+4\sqrt{185}}{-1}
$