2x^2-1000x+1000=0

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

2x^2-1000x+1000=0

a = 2; b = -1000; c = +1000;
Δ = b2-4ac
Δ = -10002-4·2·1000
Δ = 992000
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:

$\sqrt{\Delta}=\sqrt{992000}=\sqrt{6400*155}=\sqrt{6400}*\sqrt{155}=80\sqrt{155}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-80\sqrt{155}}{2*2}=\frac{1000-80\sqrt{155}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+80\sqrt{155}}{2*2}=\frac{1000+80\sqrt{155}}{4}
$