z2+12z+21=0

Solution for z2+12z+21=0 equation:

z2+12z+21=0

We add all the numbers together, and all the variables

z^2+12z+21=0

a = 1; b = 12; c = +21;
Δ = b2-4ac
Δ = 122-4·1·21
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{15}}{2*1}=\frac{-12-2\sqrt{15}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{15}}{2*1}=\frac{-12+2\sqrt{15}}{2}
$