S(t)=100t^2-300t

Solution for S(t)=100t^2-300t equation:

(S)=100S^2-300S

We move all terms to the left:

(S)-(100S^2-300S)=0

We get rid of parentheses

-100S^2+S+300S=0

We add all the numbers together, and all the variables

-100S^2+301S=0

a = -100; b = 301; c = 0;
Δ = b2-4ac
Δ = 3012-4·(-100)·0
Δ = 90601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{90601}=301$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(301)-301}{2*-100}=\frac{-602}{-200}
=3+1/100
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(301)+301}{2*-100}=\frac{0}{-200}
=0
$