0=12x^2-44x+2

Solution for 0=12x^2-44x+2 equation:

0=12x^2-44x+2

We move all terms to the left:

0-(12x^2-44x+2)=0

We add all the numbers together, and all the variables

-(12x^2-44x+2)=0

We get rid of parentheses

-12x^2+44x-2=0

a = -12; b = 44; c = -2;
Δ = b2-4ac
Δ = 442-4·(-12)·(-2)
Δ = 1840
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:

$\sqrt{\Delta}=\sqrt{1840}=\sqrt{16*115}=\sqrt{16}*\sqrt{115}=4\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{115}}{2*-12}=\frac{-44-4\sqrt{115}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{115}}{2*-12}=\frac{-44+4\sqrt{115}}{-24}
$