z^2-1000z-60775=0

Solution for z^2-1000z-60775=0 equation:

z^2-1000z-60775=0

a = 1; b = -1000; c = -60775;
Δ = b2-4ac
Δ = -10002-4·1·(-60775)
Δ = 1243100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1243100}=\sqrt{100*12431}=\sqrt{100}*\sqrt{12431}=10\sqrt{12431}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-10\sqrt{12431}}{2*1}=\frac{1000-10\sqrt{12431}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+10\sqrt{12431}}{2*1}=\frac{1000+10\sqrt{12431}}{2}
$