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

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

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

We move all terms to the left:

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

We get rid of parentheses

16t^2+85t-85=0

a = 16; b = 85; c = -85;
Δ = b2-4ac
Δ = 852-4·16·(-85)
Δ = 12665
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{-(85)-\sqrt{12665}}{2*16}=\frac{-85-\sqrt{12665}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+\sqrt{12665}}{2*16}=\frac{-85+\sqrt{12665}}{32}
$