-S=10t+4t^2

Solution for -S=10t+4t^2 equation:

-=10S+4S^2

We move all terms to the left:

--(10S+4S^2)=0

We add all the numbers together, and all the variables

-(10S+4S^2)=0

We get rid of parentheses

-4S^2-10S=0

a = -4; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-4)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-4}=\frac{0}{-8}
=0
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-4}=\frac{20}{-8}
=-2+1/2
$