T=-16t^2+68t+6

Solution for T=-16t^2+68t+6 equation:

=-16T^2+68T+6

We move all terms to the left:

-(-16T^2+68T+6)=0

We get rid of parentheses

16T^2-68T-6=0

a = 16; b = -68; c = -6;
Δ = b2-4ac
Δ = -682-4·16·(-6)
Δ = 5008
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:

$\sqrt{\Delta}=\sqrt{5008}=\sqrt{16*313}=\sqrt{16}*\sqrt{313}=4\sqrt{313}$
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-4\sqrt{313}}{2*16}=\frac{68-4\sqrt{313}}{32}
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+4\sqrt{313}}{2*16}=\frac{68+4\sqrt{313}}{32}
$