(5a-1)*(5a-1)=20

Solution for (5a-1)*(5a-1)=20 equation:

(5a-1)(5a-1)=20

We move all terms to the left:

(5a-1)(5a-1)-(20)=0

We multiply parentheses ..

(+25a^2-5a-5a+1)-20=0

We get rid of parentheses

25a^2-5a-5a+1-20=0

We add all the numbers together, and all the variables

25a^2-10a-19=0

a = 25; b = -10; c = -19;
Δ = b2-4ac
Δ = -102-4·25·(-19)
Δ = 2000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-20\sqrt{5}}{2*25}=\frac{10-20\sqrt{5}}{50}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+20\sqrt{5}}{2*25}=\frac{10+20\sqrt{5}}{50}
$