12=16t^2+24t+4

Solution for 12=16t^2+24t+4 equation:

12=16t^2+24t+4

We move all terms to the left:

12-(16t^2+24t+4)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-16t^2-24t+8=0

a = -16; b = -24; c = +8;
Δ = b2-4ac
Δ = -242-4·(-16)·8
Δ = 1088
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1088}=\sqrt{64*17}=\sqrt{64}*\sqrt{17}=8\sqrt{17}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{17}}{2*-16}=\frac{24-8\sqrt{17}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{17}}{2*-16}=\frac{24+8\sqrt{17}}{-32}
$