z^2+24+14z=0

Solution for z^2+24+14z=0 equation:

z^2+24+14z=0

a = 1; b = 14; c = +24;
Δ = b2-4ac
Δ = 142-4·1·24
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10}{2*1}=\frac{-24}{2}
=-12
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10}{2*1}=\frac{-4}{2}
=-2
$