4x(3-4x)-2x(4-4x)=-3

Solution for 4x(3-4x)-2x(4-4x)=-3 equation:

4x(3-4x)-2x(4-4x)=-3

We move all terms to the left:

4x(3-4x)-2x(4-4x)-(-3)=0

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-16x^2+8x^2+12x-8x+3=0

We add all the numbers together, and all the variables

-8x^2+4x+3=0

a = -8; b = 4; c = +3;
Δ = b2-4ac
Δ = 42-4·(-8)·3
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{7}}{2*-8}=\frac{-4-4\sqrt{7}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{7}}{2*-8}=\frac{-4+4\sqrt{7}}{-16}
$