12y^2-16y-12=0

Solution for 12y^2-16y-12=0 equation:

12y^2-16y-12=0

a = 12; b = -16; c = -12;
Δ = b2-4ac
Δ = -162-4·12·(-12)
Δ = 832
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{13}}{2*12}=\frac{16-8\sqrt{13}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{13}}{2*12}=\frac{16+8\sqrt{13}}{24}
$