850=-16.1t^2+5.8t+850

Solution for 850=-16.1t^2+5.8t+850 equation:

850=-16.1t^2+5.8t+850

We move all terms to the left:

850-(-16.1t^2+5.8t+850)=0

We get rid of parentheses

16.1t^2-5.8t-850+850=0

We add all the numbers together, and all the variables

16.1t^2-5.8t=0

a = 16.1; b = -5.8; c = 0;
Δ = b2-4ac
Δ = -5.82-4·16.1·0
Δ = 33.64
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{-(-5.8)-\sqrt{33.64}}{2*16.1}=\frac{5.8-\sqrt{33.64}}{32.2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.8)+\sqrt{33.64}}{2*16.1}=\frac{5.8+\sqrt{33.64}}{32.2}
$