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

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

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

We multiply parentheses ..

2(+3x^2+18x-1x-6)=0

We multiply parentheses

6x^2+36x-2x-12=0

We add all the numbers together, and all the variables

6x^2+34x-12=0

a = 6; b = 34; c = -12;
Δ = b2-4ac
Δ = 342-4·6·(-12)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-38}{2*6}=\frac{-72}{12}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+38}{2*6}=\frac{4}{12}
=1/3
$