(4x-1)*(4x-1)=20

Solution for (4x-1)*(4x-1)=20 equation:

(4x-1)(4x-1)=20

We move all terms to the left:

(4x-1)(4x-1)-(20)=0

We multiply parentheses ..

(+16x^2-4x-4x+1)-20=0

We get rid of parentheses

16x^2-4x-4x+1-20=0

We add all the numbers together, and all the variables

16x^2-8x-19=0

a = 16; b = -8; c = -19;
Δ = b2-4ac
Δ = -82-4·16·(-19)
Δ = 1280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16\sqrt{5}}{2*16}=\frac{8-16\sqrt{5}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16\sqrt{5}}{2*16}=\frac{8+16\sqrt{5}}{32}
$