(1-2x)x-4x(x+6)=0

Solution for (1-2x)x-4x(x+6)=0 equation:

(1-2x)x-4x(x+6)=0

We add all the numbers together, and all the variables

(-2x+1)x-4x(x+6)=0

We multiply parentheses

-2x^2-4x^2+x-24x=0

We add all the numbers together, and all the variables

-6x^2-23x=0

a = -6; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·(-6)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*-6}=\frac{46}{-12}
=-3+5/6
$