0=-12t^2+44t+16

Solution for 0=-12t^2+44t+16 equation:

0=-12t^2+44t+16

We move all terms to the left:

0-(-12t^2+44t+16)=0

We add all the numbers together, and all the variables

-(-12t^2+44t+16)=0

We get rid of parentheses

12t^2-44t-16=0

a = 12; b = -44; c = -16;
Δ = b2-4ac
Δ = -442-4·12·(-16)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-52}{2*12}=\frac{-8}{24}
=-1/3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+52}{2*12}=\frac{96}{24}
=4
$