(2x-1)(2x-1)=81

Solution for (2x-1)(2x-1)=81 equation:

(2x-1)(2x-1)=81

We move all terms to the left:

(2x-1)(2x-1)-(81)=0

We multiply parentheses ..

(+4x^2-2x-2x+1)-81=0

We get rid of parentheses

4x^2-2x-2x+1-81=0

We add all the numbers together, and all the variables

4x^2-4x-80=0

a = 4; b = -4; c = -80;
Δ = b2-4ac
Δ = -42-4·4·(-80)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-36}{2*4}=\frac{-32}{8}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+36}{2*4}=\frac{40}{8}
=5
$