0.5x^2-1000=0

Solution for 0.5x^2-1000=0 equation:

0.5x^2-1000=0

a = 0.5; b = 0; c = -1000;
Δ = b2-4ac
Δ = 02-4·0.5·(-1000)
Δ = 2000
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:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{5}}{2*0.5}=\frac{0-20\sqrt{5}}{1}
=-\frac{20\sqrt{5}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{5}}{2*0.5}=\frac{0+20\sqrt{5}}{1}
=\frac{20\sqrt{5}}{1}
$