S(t)=14t^2

Solution for S(t)=14t^2 equation:

(S)=14S^2

We move all terms to the left:

(S)-(14S^2)=0

determiningTheFunctionDomain
-14S^2+S=0

a = -14; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-14)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-14}=\frac{-2}{-28}
=1/14
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-14}=\frac{0}{-28}
=0
$