S(x)=60+29.4x-9.8x^2

Solution for S(x)=60+29.4x-9.8x^2 equation:

(S)=60+29.4S-9.8S^2

We move all terms to the left:

(S)-(60+29.4S-9.8S^2)=0

We get rid of parentheses

9.8S^2-29.4S+S-60=0

We add all the numbers together, and all the variables

9.8S^2-28.4S-60=0

a = 9.8; b = -28.4; c = -60;
Δ = b2-4ac
Δ = -28.42-4·9.8·(-60)
Δ = 3158.56
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28.4)-\sqrt{3158.56}}{2*9.8}=\frac{28.4-\sqrt{3158.56}}{19.6}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28.4)+\sqrt{3158.56}}{2*9.8}=\frac{28.4+\sqrt{3158.56}}{19.6}
$