F(t)=100-4.9t2

Solution for F(t)=100-4.9t2 equation:

(F)=100-4.9F^2

We move all terms to the left:

(F)-(100-4.9F^2)=0

We get rid of parentheses

4.9F^2+F-100=0

a = 4.9; b = 1; c = -100;
Δ = b2-4ac
Δ = 12-4·4.9·(-100)
Δ = 1961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1961}=\sqrt{1*1961}=\sqrt{1}*\sqrt{1961}=1\sqrt{1961}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1\sqrt{1961}}{2*4.9}=\frac{-1-1\sqrt{1961}}{9.8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1\sqrt{1961}}{2*4.9}=\frac{-1+1\sqrt{1961}}{9.8}
$