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

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

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

We multiply parentheses ..

-3(+4x^2-8x+x-2)=0

We multiply parentheses

-12x^2+24x-3x+6=0

We add all the numbers together, and all the variables

-12x^2+21x+6=0

a = -12; b = 21; c = +6;
Δ = b2-4ac
Δ = 212-4·(-12)·6
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-27}{2*-12}=\frac{-48}{-24}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+27}{2*-12}=\frac{6}{-24}
=-1/4
$