x^2-1000x-800000=0

Solution for x^2-1000x-800000=0 equation:

x^2-1000x-800000=0

a = 1; b = -1000; c = -800000;
Δ = b2-4ac
Δ = -10002-4·1·(-800000)
Δ = 4200000
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:

$\sqrt{\Delta}=\sqrt{4200000}=\sqrt{40000*105}=\sqrt{40000}*\sqrt{105}=200\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-200\sqrt{105}}{2*1}=\frac{1000-200\sqrt{105}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+200\sqrt{105}}{2*1}=\frac{1000+200\sqrt{105}}{2}
$