0=6-20x+12x^2

Solution for 0=6-20x+12x^2 equation:

0=6-20x+12x^2

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

a = -12; b = 20; c = -6;
Δ = b2-4ac
Δ = 202-4·(-12)·(-6)
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*-12}=\frac{-20-4\sqrt{7}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{7}}{2*-12}=\frac{-20+4\sqrt{7}}{-24}
$