2(x-3)(4x-1)=0

Solution for 2(x-3)(4x-1)=0 equation:

2(x-3)(4x-1)=0

We multiply parentheses ..

2(+4x^2-1x-12x+3)=0

We multiply parentheses

8x^2-2x-24x+6=0

We add all the numbers together, and all the variables

8x^2-26x+6=0

a = 8; b = -26; c = +6;
Δ = b2-4ac
Δ = -262-4·8·6
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-22}{2*8}=\frac{4}{16}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+22}{2*8}=\frac{48}{16}
=3
$