z2+20z+84=

Solution for z2+20z+84= equation:

z2+20z+84=

We move all terms to the left:

z2+20z+84-()=0

We add all the numbers together, and all the variables

z^2+20z=0

a = 1; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·1·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*1}=\frac{-40}{2}
=-20
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*1}=\frac{0}{2}
=0
$