S=60+2t-10t2

Solution for S=60+2t-10t2 equation:

=60+2S-10S^2

We move all terms to the left:

-(60+2S-10S^2)=0

We get rid of parentheses

10S^2-2S-60=0

a = 10; b = -2; c = -60;
Δ = b2-4ac
Δ = -22-4·10·(-60)
Δ = 2404
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:

$\sqrt{\Delta}=\sqrt{2404}=\sqrt{4*601}=\sqrt{4}*\sqrt{601}=2\sqrt{601}$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{601}}{2*10}=\frac{2-2\sqrt{601}}{20}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{601}}{2*10}=\frac{2+2\sqrt{601}}{20}
$