2x^2-1000x+50000=0

Solution for 2x^2-1000x+50000=0 equation:

2x^2-1000x+50000=0

a = 2; b = -1000; c = +50000;
Δ = b2-4ac
Δ = -10002-4·2·50000
Δ = 600000
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:

$\sqrt{\Delta}=\sqrt{600000}=\sqrt{40000*15}=\sqrt{40000}*\sqrt{15}=200\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-200\sqrt{15}}{2*2}=\frac{1000-200\sqrt{15}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+200\sqrt{15}}{2*2}=\frac{1000+200\sqrt{15}}{4}
$