S=30+49t-4.9t^2

Solution for S=30+49t-4.9t^2 equation:

=30+49S-4.9S^2

We move all terms to the left:

-(30+49S-4.9S^2)=0

We get rid of parentheses

4.9S^2-49S-30=0

a = 4.9; b = -49; c = -30;
Δ = b2-4ac
Δ = -492-4·4.9·(-30)
Δ = 2989
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2989}=\sqrt{49*61}=\sqrt{49}*\sqrt{61}=7\sqrt{61}$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-7\sqrt{61}}{2*4.9}=\frac{49-7\sqrt{61}}{9.8}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+7\sqrt{61}}{2*4.9}=\frac{49+7\sqrt{61}}{9.8}
$