z^2+14z-143=0

Solution for z^2+14z-143=0 equation:

z^2+14z-143=0

a = 1; b = 14; c = -143;
Δ = b2-4ac
Δ = 142-4·1·(-143)
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-16\sqrt{3}}{2*1}=\frac{-14-16\sqrt{3}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+16\sqrt{3}}{2*1}=\frac{-14+16\sqrt{3}}{2}
$