12-2x(3x-1)=-4

Solution for 12-2x(3x-1)=-4 equation:

12-2x(3x-1)=-4

We move all terms to the left:

12-2x(3x-1)-(-4)=0

We add all the numbers together, and all the variables

-2x(3x-1)+16=0

We multiply parentheses

-6x^2+2x+16=0

a = -6; b = 2; c = +16;
Δ = b2-4ac
Δ = 22-4·(-6)·16
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{97}}{2*-6}=\frac{-2-2\sqrt{97}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{97}}{2*-6}=\frac{-2+2\sqrt{97}}{-12}
$