0=3x^2-12x+11

Solution for 0=3x^2-12x+11 equation:

0=3x^2-12x+11

We move all terms to the left:

0-(3x^2-12x+11)=0

We add all the numbers together, and all the variables

-(3x^2-12x+11)=0

We get rid of parentheses

-3x^2+12x-11=0

a = -3; b = 12; c = -11;
Δ = b2-4ac
Δ = 122-4·(-3)·(-11)
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{3}}{2*-3}=\frac{-12-2\sqrt{3}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{3}}{2*-3}=\frac{-12+2\sqrt{3}}{-6}
$