2(x-3)(2x-1)=2

Solution for 2(x-3)(2x-1)=2 equation:

2(x-3)(2x-1)=2

We move all terms to the left:

2(x-3)(2x-1)-(2)=0

We multiply parentheses ..

2(+2x^2-1x-6x+3)-2=0

We multiply parentheses

4x^2-2x-12x+6-2=0

We add all the numbers together, and all the variables

4x^2-14x+4=0

a = 4; b = -14; c = +4;
Δ = b2-4ac
Δ = -142-4·4·4
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{33}}{2*4}=\frac{14-2\sqrt{33}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{33}}{2*4}=\frac{14+2\sqrt{33}}{8}
$