100=-4.9t^2+45t

Solution for 100=-4.9t^2+45t equation:

100=-4.9t^2+45t

We move all terms to the left:

100-(-4.9t^2+45t)=0

We get rid of parentheses

4.9t^2-45t+100=0

a = 4.9; b = -45; c = +100;
Δ = b2-4ac
Δ = -452-4·4.9·100
Δ = 65
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{-(-45)-\sqrt{65}}{2*4.9}=\frac{45-\sqrt{65}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{65}}{2*4.9}=\frac{45+\sqrt{65}}{9.8}
$