0=-0.5x^2+240x-500

Solution for 0=-0.5x^2+240x-500 equation:

0=-0.5x^2+240x-500

We move all terms to the left:

0-(-0.5x^2+240x-500)=0

We add all the numbers together, and all the variables

-(-0.5x^2+240x-500)=0

We get rid of parentheses

0.5x^2-240x+500=0

a = 0.5; b = -240; c = +500;
Δ = b2-4ac
Δ = -2402-4·0.5·500
Δ = 56600
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:

$\sqrt{\Delta}=\sqrt{56600}=\sqrt{100*566}=\sqrt{100}*\sqrt{566}=10\sqrt{566}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-10\sqrt{566}}{2*0.5}=\frac{240-10\sqrt{566}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+10\sqrt{566}}{2*0.5}=\frac{240+10\sqrt{566}}{1}
$