12-24+2y^2-16y-4=0

Solution for 12-24+2y^2-16y-4=0 equation:

12-24+2y^2-16y-4=0

We add all the numbers together, and all the variables

2y^2-16y-16=0

a = 2; b = -16; c = -16;
Δ = b2-4ac
Δ = -162-4·2·(-16)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{6}}{2*2}=\frac{16-8\sqrt{6}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{6}}{2*2}=\frac{16+8\sqrt{6}}{4}
$