5z(z-3)=10z

Solution for 5z(z-3)=10z equation:

5z(z-3)=10z

We move all terms to the left:

5z(z-3)-(10z)=0

We add all the numbers together, and all the variables

-10z+5z(z-3)=0

We multiply parentheses

5z^2-10z-15z=0

We add all the numbers together, and all the variables

5z^2-25z=0

a = 5; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·5·0
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*5}=\frac{0}{10}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*5}=\frac{50}{10}
=5
$