144=16t^2+96t+4

Solution for 144=16t^2+96t+4 equation:

144=16t^2+96t+4

We move all terms to the left:

144-(16t^2+96t+4)=0

We get rid of parentheses

-16t^2-96t-4+144=0

We add all the numbers together, and all the variables

-16t^2-96t+140=0

a = -16; b = -96; c = +140;
Δ = b2-4ac
Δ = -962-4·(-16)·140
Δ = 18176
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:

$\sqrt{\Delta}=\sqrt{18176}=\sqrt{256*71}=\sqrt{256}*\sqrt{71}=16\sqrt{71}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-16\sqrt{71}}{2*-16}=\frac{96-16\sqrt{71}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+16\sqrt{71}}{2*-16}=\frac{96+16\sqrt{71}}{-32}
$