z^2-16z=-21

Solution for z^2-16z=-21 equation:

z^2-16z=-21

We move all terms to the left:

z^2-16z-(-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}
$