z^2-14z-74=0

Solution for z^2-14z-74=0 equation:

z^2-14z-74=0

a = 1; b = -14; c = -74;
Δ = b2-4ac
Δ = -142-4·1·(-74)
Δ = 492
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:

$\sqrt{\Delta}=\sqrt{492}=\sqrt{4*123}=\sqrt{4}*\sqrt{123}=2\sqrt{123}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{123}}{2*1}=\frac{14-2\sqrt{123}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{123}}{2*1}=\frac{14+2\sqrt{123}}{2}
$