6x-2x(3x-7)=12

Solution for 6x-2x(3x-7)=12 equation:

6x-2x(3x-7)=12

We move all terms to the left:

6x-2x(3x-7)-(12)=0

We multiply parentheses

-6x^2+6x+14x-12=0

We add all the numbers together, and all the variables

-6x^2+20x-12=0

a = -6; b = 20; c = -12;
Δ = b2-4ac
Δ = 202-4·(-6)·(-12)
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{-(20)-4\sqrt{7}}{2*-6}=\frac{-20-4\sqrt{7}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{7}}{2*-6}=\frac{-20+4\sqrt{7}}{-12}
$