25z(z-4)=5z-5

Solution for 25z(z-4)=5z-5 equation:

25z(z-4)=5z-5

We move all terms to the left:

25z(z-4)-(5z-5)=0

We multiply parentheses

25z^2-100z-(5z-5)=0

We get rid of parentheses

25z^2-100z-5z+5=0

We add all the numbers together, and all the variables

25z^2-105z+5=0

a = 25; b = -105; c = +5;
Δ = b2-4ac
Δ = -1052-4·25·5
Δ = 10525
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:

$\sqrt{\Delta}=\sqrt{10525}=\sqrt{25*421}=\sqrt{25}*\sqrt{421}=5\sqrt{421}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-5\sqrt{421}}{2*25}=\frac{105-5\sqrt{421}}{50}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+5\sqrt{421}}{2*25}=\frac{105+5\sqrt{421}}{50}
$