5.5=-16.1t^2+5.8t+850

Solution for 5.5=-16.1t^2+5.8t+850 equation:

5.5=-16.1t^2+5.8t+850

We move all terms to the left:

5.5-(-16.1t^2+5.8t+850)=0

We get rid of parentheses

16.1t^2-5.8t-850+5.5=0

We add all the numbers together, and all the variables

16.1t^2-5.8t-844.5=0

a = 16.1; b = -5.8; c = -844.5;
Δ = b2-4ac
Δ = -5.82-4·16.1·(-844.5)
Δ = 54419.44
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{54419.44}}{2*16.1}=\frac{5.8-\sqrt{54419.44}}{32.2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.8)+\sqrt{54419.44}}{2*16.1}=\frac{5.8+\sqrt{54419.44}}{32.2}
$