Z^3+5z^2+9z+5=0

Solution for Z^3+5z^2+9z+5=0 equation:

^3+5Z^2+9Z+5=0

We add all the numbers together, and all the variables

5Z^2+9Z=0

a = 5; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·5·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$Z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*5}=\frac{-18}{10}
=-1+4/5
$
$Z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*5}=\frac{0}{10}
=0
$