12r^2-12r+2=0

Solution for 12r^2-12r+2=0 equation:

12r^2-12r+2=0

a = 12; b = -12; c = +2;
Δ = b2-4ac
Δ = -122-4·12·2
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{3}}{2*12}=\frac{12-4\sqrt{3}}{24}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{3}}{2*12}=\frac{12+4\sqrt{3}}{24}
$