5(1-2x)-3x(4+4x)=0

Solution for 5(1-2x)-3x(4+4x)=0 equation:

5(1-2x)-3x(4+4x)=0

We add all the numbers together, and all the variables

5(-2x+1)-3x(4x+4)=0

We multiply parentheses

-12x^2-10x-12x+5=0

We add all the numbers together, and all the variables

-12x^2-22x+5=0

a = -12; b = -22; c = +5;
Δ = b2-4ac
Δ = -222-4·(-12)·5
Δ = 724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{181}}{2*-12}=\frac{22-2\sqrt{181}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{181}}{2*-12}=\frac{22+2\sqrt{181}}{-24}
$