(5y-5)(5y-5)=125

Solution for (5y-5)(5y-5)=125 equation:

(5y-5)(5y-5)=125

We move all terms to the left:

(5y-5)(5y-5)-(125)=0

We multiply parentheses ..

(+25y^2-25y-25y+25)-125=0

We get rid of parentheses

25y^2-25y-25y+25-125=0

We add all the numbers together, and all the variables

25y^2-50y-100=0

a = 25; b = -50; c = -100;
Δ = b2-4ac
Δ = -502-4·25·(-100)
Δ = 12500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12500}=\sqrt{2500*5}=\sqrt{2500}*\sqrt{5}=50\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50\sqrt{5}}{2*25}=\frac{50-50\sqrt{5}}{50}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50\sqrt{5}}{2*25}=\frac{50+50\sqrt{5}}{50}
$