t=-16t^2+85

Solution for t=-16t^2+85 equation:

t=-16t^2+85

We move all terms to the left:

t-(-16t^2+85)=0

We get rid of parentheses

16t^2+t-85=0

a = 16; b = 1; c = -85;
Δ = b2-4ac
Δ = 12-4·16·(-85)
Δ = 5441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{5441}}{2*16}=\frac{-1-\sqrt{5441}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{5441}}{2*16}=\frac{-1+\sqrt{5441}}{32}
$