z^2-38z-250=0

Solution for z^2-38z-250=0 equation:

z^2-38z-250=0

a = 1; b = -38; c = -250;
Δ = b2-4ac
Δ = -382-4·1·(-250)
Δ = 2444
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:

$\sqrt{\Delta}=\sqrt{2444}=\sqrt{4*611}=\sqrt{4}*\sqrt{611}=2\sqrt{611}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{611}}{2*1}=\frac{38-2\sqrt{611}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{611}}{2*1}=\frac{38+2\sqrt{611}}{2}
$