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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We add all the numbers together, and all the variables

-3x^2-11x=0

a = -3; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-3)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-3}=\frac{0}{-6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-3}=\frac{22}{-6}
=-3+2/3
$