S(t)=-49t^2-98t+735

Solution for S(t)=-49t^2-98t+735 equation:

(S)=-49S^2-98S+735

We move all terms to the left:

(S)-(-49S^2-98S+735)=0

We get rid of parentheses

49S^2+98S+S-735=0

We add all the numbers together, and all the variables

49S^2+99S-735=0

a = 49; b = 99; c = -735;
Δ = b2-4ac
Δ = 992-4·49·(-735)
Δ = 153861
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(99)-\sqrt{153861}}{2*49}=\frac{-99-\sqrt{153861}}{98}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(99)+\sqrt{153861}}{2*49}=\frac{-99+\sqrt{153861}}{98}
$