S(t)=t^2-6t

Solution for S(t)=t^2-6t equation:

(S)=S^2-6S

We move all terms to the left:

(S)-(S^2-6S)=0

We get rid of parentheses

-S^2+S+6S=0

We add all the numbers together, and all the variables

-1S^2+7S=0

a = -1; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-1)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-1}=\frac{-14}{-2}
=+7
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-1}=\frac{0}{-2}
=0
$