-16t^2+100t+85=0

Solution for -16t^2+100t+85=0 equation:

-16t^2+100t+85=0

a = -16; b = 100; c = +85;
Δ = b2-4ac
Δ = 1002-4·(-16)·85
Δ = 15440
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:

$\sqrt{\Delta}=\sqrt{15440}=\sqrt{16*965}=\sqrt{16}*\sqrt{965}=4\sqrt{965}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-4\sqrt{965}}{2*-16}=\frac{-100-4\sqrt{965}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+4\sqrt{965}}{2*-16}=\frac{-100+4\sqrt{965}}{-32}
$