Z^3+25=z^2+25z

Solution for Z^3+25=z^2+25z equation:

^3+25=Z^2+25Z

We move all terms to the left:

^3+25-(Z^2+25Z)=0

We add all the numbers together, and all the variables

-(Z^2+25Z)=0

We get rid of parentheses

-Z^2-25Z=0

We add all the numbers together, and all the variables

-1Z^2-25Z=0

a = -1; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·(-1)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$Z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*-1}=\frac{0}{-2}
=0
$
$Z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*-1}=\frac{50}{-2}
=-25
$