F=30t-4.9t^2

Solution for F=30t-4.9t^2 equation:

=30F-4.9F^2

We move all terms to the left:

-(30F-4.9F^2)=0

We get rid of parentheses

4.9F^2-30F=0

a = 4.9; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·4.9·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*4.9}=\frac{0}{9.8}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*4.9}=\frac{60}{9.8}
=6+1/8.1666666666667
$