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

Solution for (3x+12)(2x-1)=0 equation:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2+21x-12=0

a = 6; b = 21; c = -12;
Δ = b2-4ac
Δ = 212-4·6·(-12)
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*6}=\frac{-48}{12}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+27}{2*6}=\frac{6}{12}
=1/2
$