0=4x(3x+1)

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

0=4x(3x+1)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(4x(3x+1)), so:

4x(3x+1)

We multiply parentheses

12x^2+4x

Back to the equation:

-(12x^2+4x)


We get rid of parentheses

-12x^2-4x=0

a = -12; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-12)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-12}=\frac{8}{-24}
=-1/3
$