z2+16z+21=0

Solution for z2+16z+21=0 equation:

z2+16z+21=0

We add all the numbers together, and all the variables

z^2+16z+21=0

a = 1; b = 16; c = +21;
Δ = b2-4ac
Δ = 162-4·1·21
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{43}}{2*1}=\frac{-16-2\sqrt{43}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{43}}{2*1}=\frac{-16+2\sqrt{43}}{2}
$