10=8.5+9.8t-4.9t^2

Solution for 10=8.5+9.8t-4.9t^2 equation:

10=8.5+9.8t-4.9t^2

We move all terms to the left:

10-(8.5+9.8t-4.9t^2)=0

We get rid of parentheses

4.9t^2-9.8t-8.5+10=0

We add all the numbers together, and all the variables

4.9t^2-9.8t+1.5=0

a = 4.9; b = -9.8; c = +1.5;
Δ = b2-4ac
Δ = -9.82-4·4.9·1.5
Δ = 66.64
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{-(-9.8)-\sqrt{66.64}}{2*4.9}=\frac{9.8-\sqrt{66.64}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9.8)+\sqrt{66.64}}{2*4.9}=\frac{9.8+\sqrt{66.64}}{9.8}
$