-45.5=-5.85t-4.9t^2

Solution for -45.5=-5.85t-4.9t^2 equation:

-45.5=-5.85t-4.9t^2

We move all terms to the left:

-45.5-(-5.85t-4.9t^2)=0

We get rid of parentheses

4.9t^2+5.85t-45.5=0

a = 4.9; b = 5.85; c = -45.5;
Δ = b2-4ac
Δ = 5.852-4·4.9·(-45.5)
Δ = 926.0225
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{-(5.85)-\sqrt{926.0225}}{2*4.9}=\frac{-5.85-\sqrt{926.0225}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.85)+\sqrt{926.0225}}{2*4.9}=\frac{-5.85+\sqrt{926.0225}}{9.8}
$