x^2-1000x+125000=0

Solution for x^2-1000x+125000=0 equation:

x^2-1000x+125000=0

a = 1; b = -1000; c = +125000;
Δ = b2-4ac
Δ = -10002-4·1·125000
Δ = 500000
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:

$\sqrt{\Delta}=\sqrt{500000}=\sqrt{250000*2}=\sqrt{250000}*\sqrt{2}=500\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-500\sqrt{2}}{2*1}=\frac{1000-500\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+500\sqrt{2}}{2*1}=\frac{1000+500\sqrt{2}}{2}
$