(12a^2)-22a-2=0

Solution for (12a^2)-22a-2=0 equation:

(12a^2)-22a-2=0

a = 12; b = -22; c = -2;
Δ = b2-4ac
Δ = -222-4·12·(-2)
Δ = 580
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{145}}{2*12}=\frac{22-2\sqrt{145}}{24}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{145}}{2*12}=\frac{22+2\sqrt{145}}{24}
$