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

Solution for 2(6x-1)(3x+2)=0 equation:

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

We multiply parentheses ..

2(+18x^2+12x-3x-2)=0

We multiply parentheses

36x^2+24x-6x-4=0

We add all the numbers together, and all the variables

36x^2+18x-4=0

a = 36; b = 18; c = -4;
Δ = b2-4ac
Δ = 182-4·36·(-4)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-30}{2*36}=\frac{-48}{72}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+30}{2*36}=\frac{12}{72}
=1/6
$