2=6+70t-16t^2

Solution for 2=6+70t-16t^2 equation:

2=6+70t-16t^2

We move all terms to the left:

2-(6+70t-16t^2)=0

We get rid of parentheses

16t^2-70t-6+2=0

We add all the numbers together, and all the variables

16t^2-70t-4=0

a = 16; b = -70; c = -4;
Δ = b2-4ac
Δ = -702-4·16·(-4)
Δ = 5156
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:

$\sqrt{\Delta}=\sqrt{5156}=\sqrt{4*1289}=\sqrt{4}*\sqrt{1289}=2\sqrt{1289}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1289}}{2*16}=\frac{70-2\sqrt{1289}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1289}}{2*16}=\frac{70+2\sqrt{1289}}{32}
$