10=28.7t-4.9t^2

Solution for 10=28.7t-4.9t^2 equation:

10=28.7t-4.9t^2

We move all terms to the left:

10-(28.7t-4.9t^2)=0

We get rid of parentheses

4.9t^2-28.7t+10=0

a = 4.9; b = -28.7; c = +10;
Δ = b2-4ac
Δ = -28.72-4·4.9·10
Δ = 627.69
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{-(-28.7)-\sqrt{627.69}}{2*4.9}=\frac{28.7-\sqrt{627.69}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28.7)+\sqrt{627.69}}{2*4.9}=\frac{28.7+\sqrt{627.69}}{9.8}
$