z^2+16z-14=0

Solution for z^2+16z-14=0 equation:

z^2+16z-14=0

a = 1; b = 16; c = -14;
Δ = b2-4ac
Δ = 162-4·1·(-14)
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{78}}{2*1}=\frac{-16-2\sqrt{78}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{78}}{2*1}=\frac{-16+2\sqrt{78}}{2}
$