1.5(12-4x^2)-2x(1-x)=8

Solution for 1.5(12-4x^2)-2x(1-x)=8 equation:

1.5(12-4x^2)-2x(1-x)=8

We move all terms to the left:

1.5(12-4x^2)-2x(1-x)-(8)=0

We add all the numbers together, and all the variables

1.5(12-4x^2)-2x(-1x+1)-8=0

We multiply parentheses

-6x^2+2x^2-2x+18-8=0

We add all the numbers together, and all the variables

-4x^2-2x+10=0

a = -4; b = -2; c = +10;
Δ = b2-4ac
Δ = -22-4·(-4)·10
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{41}}{2*-4}=\frac{2-2\sqrt{41}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{41}}{2*-4}=\frac{2+2\sqrt{41}}{-8}
$