12=-16t^2+136t

Solution for 12=-16t^2+136t equation:

12=-16t^2+136t

We move all terms to the left:

12-(-16t^2+136t)=0

We get rid of parentheses

16t^2-136t+12=0

a = 16; b = -136; c = +12;
Δ = b2-4ac
Δ = -1362-4·16·12
Δ = 17728
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:

$\sqrt{\Delta}=\sqrt{17728}=\sqrt{64*277}=\sqrt{64}*\sqrt{277}=8\sqrt{277}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-136)-8\sqrt{277}}{2*16}=\frac{136-8\sqrt{277}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-136)+8\sqrt{277}}{2*16}=\frac{136+8\sqrt{277}}{32}
$