2x(2x-1)=2

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

2x(2x-1)=2

We move all terms to the left:

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

We multiply parentheses

4x^2-2x-2=0

a = 4; b = -2; c = -2;
Δ = b2-4ac
Δ = -22-4·4·(-2)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6}{2*4}=\frac{-4}{8}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6}{2*4}=\frac{8}{8}
=1
$