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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

16t^2-69t-6=0

a = 16; b = -69; c = -6;
Δ = b2-4ac
Δ = -692-4·16·(-6)
Δ = 5145
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:

$\sqrt{\Delta}=\sqrt{5145}=\sqrt{49*105}=\sqrt{49}*\sqrt{105}=7\sqrt{105}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-7\sqrt{105}}{2*16}=\frac{69-7\sqrt{105}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+7\sqrt{105}}{2*16}=\frac{69+7\sqrt{105}}{32}
$