2=-16t^2+126t

Solution for 2=-16t^2+126t equation:

2=-16t^2+126t

We move all terms to the left:

2-(-16t^2+126t)=0

We get rid of parentheses

16t^2-126t+2=0

a = 16; b = -126; c = +2;
Δ = b2-4ac
Δ = -1262-4·16·2
Δ = 15748
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:

$\sqrt{\Delta}=\sqrt{15748}=\sqrt{4*3937}=\sqrt{4}*\sqrt{3937}=2\sqrt{3937}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-2\sqrt{3937}}{2*16}=\frac{126-2\sqrt{3937}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+2\sqrt{3937}}{2*16}=\frac{126+2\sqrt{3937}}{32}
$