2z^2+20z+2=0

Solution for 2z^2+20z+2=0 equation:

2z^2+20z+2=0

a = 2; b = 20; c = +2;
Δ = b2-4ac
Δ = 202-4·2·2
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-8\sqrt{6}}{2*2}=\frac{-20-8\sqrt{6}}{4}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+8\sqrt{6}}{2*2}=\frac{-20+8\sqrt{6}}{4}
$