(2x^2)-12x+1=-11

Solution for (2x^2)-12x+1=-11 equation:

(2x^2)-12x+1=-11

We move all terms to the left:

(2x^2)-12x+1-(-11)=0

We add all the numbers together, and all the variables

2x^2-12x+12=0

a = 2; b = -12; c = +12;
Δ = b2-4ac
Δ = -122-4·2·12
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{3}}{2*2}=\frac{12-4\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{3}}{2*2}=\frac{12+4\sqrt{3}}{4}
$